{ "cells": [ { "cell_type": "markdown", "id": "4769054f-d675-4678-852f-945df5f1fc7d", "metadata": {}, "source": [ "
Peter Norvig, December 2025
\n", "\n", "# Advent of Code 2025\n", "\n", "I enjoy doing the [**Advent of Code**](https://adventofcode.com/) (AoC) programming puzzles, so here we go for 2025! \n", "\n", "This year I will be doing something different: I will solve each problem myself here, and then [**in another notebook**](Advent-2025-AI.ipynb) I will ask an AI Large Language Model to solve the same problem. Check out the differences!\n", "\n", "# Day 0\n", "\n", "I'm glad that [@GaryGrady](https://mastodon.social/@garygrady) is providing cartoons:\n", "\n", "\"Gary\n", "\n", "I start by loading up my [**AdventUtils.ipynb**](AdventUtils.ipynb) notebook (same as last time except for the `current_year`). On each day I will first parse the input (with the help of my `parse` utility function), then solve Part 1 and Part 2 (recording the correct answer with my `answer` function)." ] }, { "cell_type": "code", "execution_count": 1, "id": "d5f1da68-5da6-434d-a068-1d93497a86b3", "metadata": {}, "outputs": [], "source": [ "%run AdventUtils.ipynb\n", "current_year = 2025" ] }, { "cell_type": "markdown", "id": "37bc12b8-d0dc-4873-984c-6f09ae647229", "metadata": {}, "source": [ "# [Day 1](https://adventofcode.com/2025/day/1): Secret Entrance\n", "\n", "On Day 1 we meet an elf and learn that our task is to finish decorating the North Pole by December 12th. There will be 24 challenges along the way; the first one involves unlocking a safe. The safe has a dial with 100 numbers, and an arrow that currently points at 50. Our input for today is a sequence of left and right rotations; for example \"R20\" means move the dial right by 20 numbers and \"L13\" means move it left by 13 numbers. I'll use my `parse` utility function to parse each line of the input as an integer, after replacing each 'L' with a minus sign and each 'R' with a plus sign:" ] }, { "cell_type": "code", "execution_count": 2, "id": "ed911a15-addc-4c04-8546-2c9f37aee341", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Puzzle input ➜ 4780 strs of size 2 to 4:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "L20\n", "L13\n", "L16\n", "L16\n", "L29\n", "L7\n", "L48\n", "L48\n", "...\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Parsed representation ➜ 4780 ints in range -999 to 997:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "-20\n", "-13\n", "-16\n", "-16\n", "-29\n", "-7\n", "-48\n", "-48\n", "...\n" ] } ], "source": [ "def parse_rotation(line: str) -> str: return int(line.replace('L', '-').replace('R', '+'))\n", "\n", "rotations = parse(day=1, parser=parse_rotation) " ] }, { "cell_type": "markdown", "id": "7c98c883-d1dc-4d4e-9590-d47b1de000a0", "metadata": {}, "source": [ "Note that my `parse` function prints the first few input lines, then prints the parsed representation of these lines. That helps me debug and helps you the reader understand what is going on.\n", "\n", "\"Gary\n", "\n", "### Part 1: How many times is the dial left pointing at 0 after any rotation in the sequence?\n", "\n", "When applying the rotations in order, we are asked how many of the rotations leave the dial pointing at 0. The `itertools.accumulate` function yields running totals of its input sequence, so we just have to count (quantify) how many times the running total of the rotations is 0 mod 100. I'll write a function to do that and run it on the input:" ] }, { "cell_type": "code", "execution_count": 3, "id": "86079e27-2912-4431-8608-7a110a115789", "metadata": {}, "outputs": [], "source": [ "def count_zeros(numbers, dial=100) -> int:\n", " \"\"\"How many zeros (modulo `dial`) in the running partial sums of the numbers?\"\"\"\n", " return quantify(total % dial == 0 for total in accumulate(numbers, initial=50))" ] }, { "cell_type": "code", "execution_count": 4, "id": "eb90f15c-8f87-4d94-b49c-fcaa53aab8ae", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1182" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "count_zeros(rotations)" ] }, { "cell_type": "markdown", "id": "b5f68a70-8465-4249-954c-cba2b78751d8", "metadata": {}, "source": [ "I submitted \"1182\" to AoC and got back *That's the right answer!*, so I record the answer (and its run time) like this:" ] }, { "cell_type": "code", "execution_count": 5, "id": "8387c4bd-a0b7-46d7-b726-d2d4b383b3cf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 1.1: .0005 seconds, answer 1182 correct" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(puzzle=1.1, solution=1182, code=lambda: \n", " count_zeros(rotations))" ] }, { "cell_type": "markdown", "id": "12d5d111-8f69-4944-855b-54cca8215d7b", "metadata": {}, "source": [ "### Part 2: How many times does the dial point to 0 at any time?\n", "\n", "For Part 2 we are asked to count both when a rotation ends up at 0 and when the arrow passes 0 at any time during a rotation. For example, if the arrow points to 95, then only a \"R5\" or a \"L95\" would register a 0 in Part 1, but now for Part 2 a rotation of \"R10\" would also count because it passes 0 (as would any rotation of \"R5\" or larger, or \"L95\" or larger). \n", "\n", "I'll start with a brute force approach: treat a rotation of, say, 20 as 20 rotations of 1, and then use the same `count_zeros` function from Part 1. (Note that `sign(r)` returns +1 for any positive input, and -1 for any negative input.)" ] }, { "cell_type": "code", "execution_count": 6, "id": "bfb5bd2d-d768-47b3-9897-d28f83f2202a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 1.2: .1417 seconds, answer 6907 correct" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(1.2, 6907, lambda:\n", " count_zeros(sign(r) for r in rotations for _ in range(abs(r))))" ] }, { "cell_type": "markdown", "id": "bb0f6906-369e-4b3c-8840-d5648d713942", "metadata": {}, "source": [ "That's a long run time for a Day 1 problem, so here's a faster method: break each rotation down into a number of full circles and some remainder, then add the full circles to the count of zeros, and add one more if the remainder is at least as much as the distance to zero (in the appropriate direction): " ] }, { "cell_type": "code", "execution_count": 7, "id": "e0b676d8-3d4f-4b36-835d-b045ece53bd6", "metadata": {}, "outputs": [], "source": [ "def zero_clicks(rotations, position=50, dial=100) -> int:\n", " \"\"\"How many times does any click cause the dial to point at 0?\n", " Count 1 if the rotation crosses the distance to 0,\n", " and for large rotations, count abs(r) // 100 more.\"\"\"\n", " zeros = 0\n", " for r in rotations:\n", " full_circles, remainder = divmod(abs(r), dial)\n", " distance_to_0 = (dial - position if (r > 0 or position == 0) else position)\n", " zeros += full_circles + (1 if remainder >= distance_to_0 else 0)\n", " position = (position + r) % dial\n", " return zeros" ] }, { "cell_type": "code", "execution_count": 8, "id": "8969191e-bd50-4187-8e4b-64524bc8427a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 1.2: .0009 seconds, answer 6907 correct" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(1.2, 6907, lambda:\n", " zero_clicks(rotations))" ] }, { "cell_type": "markdown", "id": "f47b1f7a-c9d9-4b21-a28a-f1e4e73d4c0d", "metadata": {}, "source": [ "That's much faster, but the code is trickier, and indeed I initially had a **bug** in the `distance_to_0` computation: when the current position is 0 the distance should be 100: it takes a full rotation to get back to 0. I fixed the bug by adding `or position == 0`." ] }, { "cell_type": "markdown", "id": "dd6908ae-1906-4687-a50d-a50293a1dad5", "metadata": {}, "source": [ "# [Day 2](https://adventofcode.com/2025/day/2): Gift Shop\n", "\n", "Today we're in the North Pole gift shop, and are asked to help the elves identify invalid product IDs on the items there. We're giving a list of ranges of product IDs of items in stock. Each range is a pair of integers separated by a dash, and the ranges are separated by commas:" ] }, { "cell_type": "code", "execution_count": 9, "id": "63bb5099-68ab-41b3-8d0c-2f409433b3f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Puzzle input ➜ 1 str of size 511:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "990244-1009337,5518069-5608946,34273134-34397466,3636295061-3636388848,8613701-8663602,573252-68 ...\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Parsed representation ➜ 35 tuples of size 2:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "(990244, 1009337)\n", "(5518069, 5608946)\n", "(34273134, 34397466)\n", "(3636295061, 3636388848)\n", "(8613701, 8663602)\n", "(573252, 688417)\n", "(472288, 533253)\n", "(960590, 988421)\n", "...\n" ] } ], "source": [ "id_ranges = parse(day=2, parser=positive_ints, sections=lambda text: text.split(','))" ] }, { "cell_type": "markdown", "id": "a5463e74-a3a1-4c79-9497-a1e307ef81e2", "metadata": {}, "source": [ "\"GaryJGrady\n", "\n", "### Part 1: What is the sum of the invalid IDs?\n", "\n", "An invalid ID is defined as one that consists of a digit sequence repeated twice. So 55, 6464 and 123123 are invalid. We're asked for the sum of the invalid IDs across all the ID ranges.\n", "\n", "We could look at every number in each range and check if the first half of the number (as a string) is the same as the second half. How many checks would that be?" ] }, { "cell_type": "code", "execution_count": 10, "id": "d682f3f2-415e-4556-b6c8-43e331a38703", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1990936" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum((hi - lo + 1) for lo, hi in id_ranges)" ] }, { "cell_type": "markdown", "id": "a9bf1aab-bd09-49a9-ab57-8b26b1f4a98d", "metadata": {}, "source": [ "Only 2 million! So it would indeed be feasible to check every one. But I have a suspicion that Part 2 would make it infeasible, so I'll invest in a more efficient approach. For each ID range, instead of enumerating every number in the range and checking each one for validity, I will instead enumerate over the *first half* of the possible digit strings, and automatically generate invalid IDs by appending a copy of the first half to itself. By *first half* I don't mean divide by 2; I mean the first half of the digit string: the first half of \"123456\" is \"123\".\n", "\n", "Suppose the range is 123456-223000. I enumerate from 123 to 223, and for each number generate an invalid ID:\n", "[123123, 124124, 125125, ... 223223]. I then yield the IDs that are within the range (in this case all but the first and the last are in the range 123456-223000). Altogether I only have to consider 101 IDs rather than 100,001. (The algorithm scales with the square root of the size of the range, not with the size of the range itself.)" ] }, { "cell_type": "code", "execution_count": 11, "id": "1345f93d-84c5-43f8-b6c2-9fc7b8f5ed90", "metadata": {}, "outputs": [], "source": [ "def invalids_in_range(lo: int, hi: int) -> Iterable[int]:\n", " \"\"\"Yield all the invalid IDs between lo and hi inclusive.\n", " An ID is invalid if it consists of a digit sequence repeated twice.\"\"\"\n", " first_half = str(lo)[:max(1, len(str(lo)) // 2)]\n", " for i in count_from(int(first_half)):\n", " id = int(str(i) * 2)\n", " if lo <= id <= hi:\n", " yield id\n", " elif id > hi:\n", " return\n", "\n", "def invalids(id_ranges) -> List[int]:\n", " \"\"\"Invalid IDs, according to any one of the list of invalid ID ranges.\"\"\"\n", " return append(invalids_in_range(lo, hi)\n", " for (lo, hi) in id_ranges)\n", "\n", "assert invalids([(11, 22)]) == [11, 22]" ] }, { "cell_type": "code", "execution_count": 12, "id": "8b0d12b3-f184-4149-8b49-f9ff78663d46", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 2.1: .0033 seconds, answer 23560874270 correct" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(2.1, 23560874270, lambda:\n", " sum(invalids(id_ranges)))" ] }, { "cell_type": "markdown", "id": "188dd774-0c2d-4304-8351-dfe208913a99", "metadata": {}, "source": [ "### Part 2: What is the sum of the invalid IDs, under the new rules?\n", "\n", "In Part 2 we discover that an ID should be considered invalid if it consists of two *or more* repeats of a sequence of digits. So 111 (1 repeated three times), 12121212 (12 repeated four times), and 222222 (2 repeated six times) are all invalid. I'll rewrite `invalids_in_range` to take an optional argument saying how many repeats we're looking for, and introduce `all_invalids` to try all possible repeat lengths:" ] }, { "cell_type": "code", "execution_count": 13, "id": "4fbf52e7-a06a-4000-8627-80d159788da1", "metadata": {}, "outputs": [], "source": [ "def invalids_in_range(lo: int, hi: int, repeat=2) -> Iterable[int]:\n", " \"\"\"Yield all the invalid IDs between lo and hi inclusive\n", " that are formed from exactly `repeat` repeated digit sequences.\"\"\"\n", " first_half = int(str(lo)[:len(str(lo)) // repeat] or 1)\n", " for i in count_from(int(first_half)):\n", " id = int(str(i) * repeat)\n", " if lo <= id <= hi:\n", " yield id\n", " elif id > hi:\n", " return\n", "\n", "def all_invalids(id_ranges) -> Set[int]:\n", " \"\"\"All Invalid IDs, according to the list of ranges, with any number of repeats.\"\"\"\n", " return union(invalids_in_range(lo, hi, repeat)\n", " for (lo, hi) in id_ranges\n", " for repeat in range(2, len(str(hi)) + 1))" ] }, { "cell_type": "markdown", "id": "1e7d71d2-8c08-4673-8d12-661edd6ab6f5", "metadata": {}, "source": [ "Since this is a bit tricky, I include some unit test assertions:" ] }, { "cell_type": "code", "execution_count": 14, "id": "5a29e5bc-3b07-4800-9a0f-4bd433e01c55", "metadata": {}, "outputs": [], "source": [ "assert list(invalids_in_range(2121212118, 2121212124, 5)) == [2121212121]\n", "assert all_invalids([(11, 22), (95, 115)]) == {11, 22, 99, 111}" ] }, { "cell_type": "markdown", "id": "cb254f91-8c6d-445d-86be-97df9a93018c", "metadata": {}, "source": [ "Now I'll verify that the answer for Part 1 still works, and go ahead and compute the answer for Part 2:" ] }, { "cell_type": "code", "execution_count": 15, "id": "8a7c6c25-4b5f-4178-8559-166ba1a9f924", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 2.1: .0027 seconds, answer 23560874270 correct" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(2.1, 23560874270, lambda:\n", " sum(invalids(id_ranges)))" ] }, { "cell_type": "code", "execution_count": 16, "id": "32fefd65-df2a-4ea3-9acd-7525ebd32380", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 2.2: .0036 seconds, answer 44143124633 correct" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(2.2, 44143124633, lambda:\n", " sum(all_invalids(id_ranges)))" ] }, { "cell_type": "markdown", "id": "872cf212-bfbf-4edd-b898-5f76ad122a85", "metadata": {}, "source": [ "I initially had another **bug** here: I initially counted \"222222\" three times: once as 2 repeats of \"222\", once as 3 repeats of \"22\", and once as 6 repeats of \"2\". I changed the output of `all_invalids` to be a `set` rather than a `list` to fix that." ] }, { "cell_type": "markdown", "id": "16e222aa-d424-44d8-bcb3-7aa11c31b540", "metadata": {}, "source": [ "# [Day 3](https://adventofcode.com/2025/day/3): Lobby\n", "\n", "Entering the lobby, we find that the elevators are offline. We might be able to fix the problem by turning on some batteries. There are multiple battery banks, each bank consisting of a sequence of batteries, each labeled with its *joltage*, a digit from 1 to 9. " ] }, { "cell_type": "code", "execution_count": 17, "id": "04ef4f2f-2b07-43cd-87d4-a8f63f7fe840", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Puzzle input ➜ 200 strs of size 100:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "5353323523322232362334333433323333353233331313222372133133353643423323233323333534414523333432223242\n", "6344544745655555456556556566665564538465555575558846455665837545764555554465564547547565544657585435\n", "2246273372253242254243532252231242225522622633532222322234255122531222423531343223123232234213323424\n", "6545643634344444495734739454433454439454355654483544243344534445434437426443854344454534654439534424\n", "2356636643143433535443636338231745346538433576334436353176353333433532345344334224435234343644332536\n", "3221311221443323323322222214632342232233222322333436263122265162212321261323142262212332322125216222\n", "3336332333336335335324359336493238433441666379243536334165623214253384333323893933867663434332383763\n", "3235321252332431332223232436222532432226223222213233432853535322314122221322352235213323124321222233\n", "...\n" ] } ], "source": [ "banks = parse(day=3)" ] }, { "cell_type": "markdown", "id": "529e9177-7e47-46fa-bdc0-b979205d2e72", "metadata": {}, "source": [ "### Part 1: What is the maximum possible total output joltage?\n", "\n", "We can turn on exactly two batteries in each bank, resulting in a two digit number which is the *joltage* of the bank. For example, given the bank \"8647\" we could choose to turn on the \"8\" and \"7\" to produce a joltage of 87; that's the maximum. The function `joltage` chooses the biggest first digit, and then the biggest second digit that follows the first digit. Note that the possible choices for the first digit exclude the last digit, because if we chose that, then there would be no choices left for the second digit. (I chose to do the string-to-int conversion in `total_joltage`; it would also be fine to have `joltage` return an int.)" ] }, { "cell_type": "code", "execution_count": 18, "id": "0168ada2-b53e-4215-9e6a-2468759f095c", "metadata": {}, "outputs": [], "source": [ "def joltage(bank: str) -> str:\n", " \"\"\"The maximum possible joltage by turning on 2 batteries in the bank.\n", " Pick the biggest first digit, then the biggest digit that follows.\"\"\"\n", " first = max(bank[:-1]) # The first digit can't be the last character\n", " second = max(bank[bank.index(first) + 1:]) # The second digit must come after the first\n", " return first + second\n", "\n", "def total_joltage(banks: List[str]) -> int:\n", " \"\"\"The maximum possible joltage from all the banks.\"\"\"\n", " return sum(int(joltage(bank)) for bank in banks)" ] }, { "cell_type": "code", "execution_count": 19, "id": "3f6390f5-78b7-4472-acf9-8855d2c2453e", "metadata": {}, "outputs": [], "source": [ "assert joltage(\"8647\") == \"87\"\n", "assert joltage(\"1119\") == \"19\"" ] }, { "cell_type": "code", "execution_count": 20, "id": "9cc62ae9-b313-4b82-b8fb-bab9c0ef5cb6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 3.1: .0006 seconds, answer 17085 correct" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(3.1, 17085, lambda:\n", " total_joltage(banks))" ] }, { "cell_type": "markdown", "id": "3f8a4645-5e36-4b3d-8ace-125024403b3b", "metadata": {}, "source": [ "### Part 2: What is the new maximum possible total output joltage?\n", "\n", "In Part 2 the elf hits the \"*joltage limit safety override*\" button, and we can now turn on 12 batteries per bank, resulting in a 12-digit joltage. What is the new maximum possible total joltage?\n", "\n", "I will make a change to the two functions, passing in the number of digits to be chosen, *n* (with default 2 for backwards compatibility). The function `joltage` recurses when there is more than one digit remaining, choosing the first digit from the bank up to the last *n* - 1 characters, then recursively finding the biggest joltage from the rest. " ] }, { "cell_type": "code", "execution_count": 21, "id": "b9507c12-421b-41af-b926-a4d3d83f622d", "metadata": {}, "outputs": [], "source": [ "def joltage(bank: str, n=2) -> str:\n", " \"\"\"The maximum possible joltage by turning on `n` batteries in the bank.\n", " Pick the first digit, then the maximum joltage from the rest of the bank.\"\"\"\n", " if n == 1:\n", " return max(bank)\n", " else:\n", " first = max(bank[:-(n - 1)]) # The first digit can't be the last n-1 characters\n", " rest = bank[bank.index(first) + 1:]\n", " return first + joltage(rest, n - 1)\n", "\n", "def total_joltage(banks: List[str], n=2) -> int:\n", " \"\"\"The maximum possible joltage from all the banks,\n", " when `n` batteries are turned on per bank.\"\"\"\n", " return sum(int(joltage(bank, n)) for bank in banks)" ] }, { "cell_type": "code", "execution_count": 22, "id": "4a58a657-8f32-4001-a4ff-f30dfbe7e5e7", "metadata": {}, "outputs": [], "source": [ "assert joltage(\"811111111111119\", 2) == '89'\n", "assert joltage(\"818181911112111\", 5) == '92111'\n", "assert joltage(\"818181911112111\", 12) == '888911112111'" ] }, { "cell_type": "markdown", "id": "28d2e2ce-98b5-4b3b-9f4d-26efcb7e1258", "metadata": {}, "source": [ "I'll make sure Part 1 still works, and then solve Part 2:" ] }, { "cell_type": "code", "execution_count": 23, "id": "fe3cff78-81c0-4d4a-bb4d-f0f841067e0d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 3.1: .0006 seconds, answer 17085 correct" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(3.1, 17085, lambda:\n", " total_joltage(banks))" ] }, { "cell_type": "code", "execution_count": 24, "id": "f971839e-81ea-49b4-a92f-a44884be645d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 3.2: .0019 seconds, answer 169408143086082 correct" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(3.2, 169408143086082, lambda:\n", " total_joltage(banks, 12))" ] }, { "cell_type": "markdown", "id": "db13a440-9ad0-4344-b555-aec969869688", "metadata": {}, "source": [ "# [Day 4](https://adventofcode.com/2025/day/4): Printing Department\n", "\n", "The floor of the printing department is divided into squares, some of which contain a roll of paper. The day's input is a map of the floor, with `@` representing a roll of paper. I can handle that with the `Grid` class from my [AdventUtils](AdventUtils.ipynb):" ] }, { "cell_type": "code", "execution_count": 25, "id": "c9f227d5-2748-48e1-80c1-7385dad46323", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Puzzle input ➜ 140 strs of size 140:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", ".@@@@@...@.@@@@@@@@@@.@@@@@@@.@.@.@@@@@@@@@@@@@..@.@@@.@@@@@@..@.@..@.@@...@.@@@@..@@@@....@@@.@ ...\n", ".@@@@@.@....@.....@@@.@@.@@.@@@.@@@.@.@.@.@@@@@.@@.@@@@@.@@@@@@@@@@@..@@.@.@@.@@@.@@@@@@@@@@@..@ ...\n", "@.@@@@.@@@@.@@@@..@@.@@@@@@@@.@@@@.@@@@.@@..@.@...@.@.@.@.@@..@@@@@.@.@.@@@@.@@@@@@@@@.@@@@..@@. ...\n", ".@.....@.@@@..@.@@@.@..@@@@@..@@@.@@..@...@.@@@@.@@@.@.@@@@@@.@.@@@@@@@.@.@@@.@@@@@@...@@.@@..@. ...\n", "@@@@@.@@@.@@@@@@@..@@.@.@@@..@@..@@@.@@....@.@..@@@@@@@@.@.@@..@@...@@.@@@...@.@.@@@..@.@.@@@@@@ ...\n", "@.@@@@@@..@@@@...@..@@@@@@.@@@..@.....@@.@.@@...@@@.@@.@.@@@....@@.@.@.@@@@.@@@@@.@@@.@@...@@.@@ ...\n", ".@@@.@.@@@..@@.@.@@@@@.@.@..@@....@..@.@.@@@@.@..@@.@..@@@@@.@@@@@@@.@.@@@.@.@@@.@@@@.@@@@@@@@.@ ...\n", "@@@@@@@.@@...@@@....@.@@@@.@@@@@@@@@.@@@.@@.@@..@...@@@@@.@@@..@.@@@@@@@@@@.@@@.@..@@@.@@@@.@.@@ ...\n", "...\n" ] } ], "source": [ "paper_grid = Grid(parse(day=4), directions=directions8)" ] }, { "cell_type": "markdown", "id": "4dd00e21-228c-41f6-a28c-e2213e60d4ce", "metadata": {}, "source": [ "\"Gary\n", "\n", "\n", "### Part 1: How many rolls of paper can be accessed by a forklift?\n", "\n", "A roll is **accessible** by forklift if there are fewer than four rolls of paper in the eight adjacent positions (that's why I specified `directions8` in defining `paper_grid`). Counting the number of accessible rolls is easy, but I decided to make `accessible rolls` return a list of positions rather than a count, in anticipation of Part 2." ] }, { "cell_type": "code", "execution_count": 26, "id": "6fe5bd44-8a28-4d7a-bc8b-edc4af8f23c3", "metadata": {}, "outputs": [], "source": [ "def accessible_rolls(grid: Grid) -> List[Point]:\n", " \"\"\"The positions of all the accessible rolls of paper on the grid.\"\"\"\n", " return [p for p in grid if is_accessible(p, grid)]\n", "\n", "def is_accessible(p: Point, grid: Grid) -> bool:\n", " \"\"\"A roll of paper is accessible if there are fewer than \n", " four rolls of paper in the eight adjacent positions.\"\"\"\n", " return grid[p] == '@' and grid.neighbor_contents(p).count('@') < 4" ] }, { "cell_type": "markdown", "id": "714b9eed-bdee-4e3f-b0be-1a3f727dddfb", "metadata": {}, "source": [ "Here's the answer:" ] }, { "cell_type": "code", "execution_count": 27, "id": "a5ef09cf-b204-41eb-80d8-de107d385dbb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 4.1: .0538 seconds, answer 1569 correct" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(4.1, 1569, lambda:\n", " len(accessible_rolls(paper_grid)))" ] }, { "cell_type": "markdown", "id": "550312ae-a70b-405c-90e6-5df9c9afc0e8", "metadata": {}, "source": [ "### Part 2: How many rolls of paper can be removed?\n", "\n", "If the elves can access a paper roll, they can remove it by forklift. That may in turn make other rolls accessible, and hence removable. How many rolls in total can be removed?\n", "\n", "It looks like I was right to make `accessible_rolls` return a list of points rather than a count! I can answer the question by repeatedly finding the accessible rolls, removing them (on a copy of the grid so I don't mess up the original grid), and repeating until there are no more accessible rolls." ] }, { "cell_type": "code", "execution_count": 28, "id": "0ed53853-268c-4c2f-a929-cb3e6005a348", "metadata": {}, "outputs": [], "source": [ "def removable_rolls(grid: Grid) -> Iterable[Point]:\n", " \"\"\"The positions of paper rolls that can be removed, in any nuber of iterations.\"\"\"\n", " grid2 = grid.copy() # To avoid mutating the original input grid\n", " points = accessible_rolls(grid2)\n", " while points:\n", " yield from points\n", " grid2.update({p: '.' for p in points})\n", " points = accessible_rolls(grid2)" ] }, { "cell_type": "code", "execution_count": 29, "id": "2fb17a51-05f7-42ec-8d6c-222121a026cf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 4.2: 1.2313 seconds, answer 9280 correct" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(4.2, 9280, lambda:\n", " quantify(removable_rolls(paper_grid))) " ] }, { "cell_type": "markdown", "id": "7143f73e-3b9b-49f3-bfa9-625899a56e37", "metadata": {}, "source": [ "That's the right answer, but the run time is slow. The main issue is that `accessible_rolls` has to look at the whole grid on every iteration. That's wasteful: If the previous iteration only removed one roll, all we really need to look at on the next iteration is the neighbors of the removed roll. So I'll keep a queue of possibly removable points and repeatedly pop a point off the queue, and if it is an accessible roll, remove it and put all its neighbors on the queue. When the queue is empty, no more rolls can be removed." ] }, { "cell_type": "code", "execution_count": 30, "id": "54f20b5e-6713-459c-8d40-e545ce6b8e42", "metadata": {}, "outputs": [], "source": [ "def removable_rolls(grid: Grid) -> Iterable[Point]:\n", " \"\"\"The positions of paper rolls that can be removed, in any nuber of iterations.\"\"\"\n", " grid2 = grid.copy() # To avoid mutating the original input grid\n", " Q = list(grid) # A queue of possibly removable positions in the grid\n", " while Q:\n", " p = Q.pop()\n", " if is_accessible(p, grid2):\n", " yield p\n", " grid2[p] = '.'\n", " Q.extend(grid2.neighbors(p))" ] }, { "cell_type": "code", "execution_count": 31, "id": "bcba970b-09aa-479b-9c6d-4f6a7ac49fed", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 4.2: .1409 seconds, answer 9280 correct" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(4.2, 9280, lambda:\n", " quantify(removable_rolls(paper_grid)))" ] }, { "cell_type": "markdown", "id": "1f9a1e40-192a-4386-8cfb-bc5f69c88a9b", "metadata": {}, "source": [ "# [Day 5](https://adventofcode.com/2025/day/5): Cafeteria\n", "\n", "Today we're in the cafeteria, and the elves need to figure out which of their ingredients are fresh or spoiled. The input file has two parts (paragraphs), the first consisting of ranges of fresh ingredient IDs, like \"6-7\" and the second consisting of the available ingredient IDs, like \"8\". I can parse the data like this:" ] }, { "cell_type": "code", "execution_count": 32, "id": "4b508db5-aeae-410e-a062-1b2d4ce41253", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Puzzle input ➜ 1184 strs of size 0 to 31:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "292632986393425-296797126337251\n", "428261559408337-431275643240865\n", "197704206528056-198822557342819\n", "36791726875734-37049023408764\n", "134880223152389-139959748438608\n", "31870818340663-32138457068292\n", "443613579514078-447616030778273\n", "284142407577672-288117756872436\n", "...\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Parsed representation ➜ 2 tuples of size 183 to 1000:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "((292632986393425, 296797126337251), (428261559408337, 431275643240865), (197704206528056, 19882 ...\n", "(92087202605588, 314304587960778, 19184152482180, 331502336245673, 104093299503920, 224082459481 ...\n" ] } ], "source": [ "def parse_ingredients(text: str) -> tuple:\n", " \"\"\"Parse either ranges like \"3-5\", or integers like \"8\".\"\"\"\n", " if '-' in text:\n", " return mapt(positive_ints, lines(text))\n", " return mapt(positive_ints, lines(text)) if '-' in text else ints(text)\n", " \n", "fresh_ranges, available_ingredient_ids = parse(day=5, parser=parse_ingredients, sections=paragraphs)" ] }, { "cell_type": "markdown", "id": "ebb61d5f-4683-4ff6-986c-69154d512e1b", "metadata": {}, "source": [ "### Part 1: How many of the available ingredient IDs are fresh?\n", "\n", "Keep it simple: For each ingredient ID, check to see if it is contained in any of the ranges (then we'll see if this is fast enough):" ] }, { "cell_type": "code", "execution_count": 33, "id": "ae5b33e4-92f5-4fe2-bd5a-6b22095724fa", "metadata": {}, "outputs": [], "source": [ "def count_fresh_ingredients(fresh_ranges, available_ingredient_ids) -> int:\n", " \"\"\"How many of the available ingredient IDs are in one of the fresh ranges?\"\"\"\n", " return quantify(any(lo <= id <= hi for (lo, hi) in fresh_ranges)\n", " for id in available_ingredient_ids)" ] }, { "cell_type": "code", "execution_count": 34, "id": "112a84f7-9bb8-45f0-9d7e-f600f37f0fdf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 5.1: .0073 seconds, answer 635 correct" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(5.1, 635, lambda:\n", " count_fresh_ingredients(fresh_ranges, available_ingredient_ids))" ] }, { "cell_type": "markdown", "id": "01c2c322-e873-412f-9c47-59ffdf9adf79", "metadata": {}, "source": [ "Fast enough! Let's move on.\n", "\n", "### Part 2: How many ingredient IDs are fresh?\n", "\n", "In Part 2 we are asked how many of the possible ingredient IDs are fresh, regardless of whether the ID is available or not. I could convert a range like \"3-5\" into the set {3, 4, 5} and then union the sets together. How many elements would be in that set? Here's an estimate: " ] }, { "cell_type": "code", "execution_count": 35, "id": "47a660d2-746c-433f-b4ae-9d01f70bc504", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "476036797138761" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(hi - lo for (lo, hi) in fresh_ranges)" ] }, { "cell_type": "markdown", "id": "1360869f-3ccb-4c71-8d00-35de1215389f", "metadata": {}, "source": [ "OK, switch to Plan B. Instead of explicitly building this set I can instead sort the fresh ID ranges (by their low number) and go through them, keeping track of the lowest ID that has not yet been explored for freshness, and a count of the fresh IDs found so far. For each range, the number of new fresh IDs is the length of the range that starts with either the start of the range or the first unexplored ID, and ends at the end of the range." ] }, { "cell_type": "code", "execution_count": 36, "id": "f52e8ecd-325e-4ed4-8928-de9365b5b7d4", "metadata": {}, "outputs": [], "source": [ "def count_fresh_ids(fresh_ranges) -> int:\n", " \"\"\"How many IDs are contained in the union of the ranges?\"\"\"\n", " fresh_count = 0 # The number of fresh IDs found so far\n", " unexplored = 0 # The highest ID number that we haven't considered yet\n", " for (lo, hi) in sorted(fresh_ranges):\n", " start = max(unexplored, lo)\n", " fresh_count += len(range(start, hi + 1))\n", " unexplored = max(unexplored, hi + 1)\n", " return fresh_count" ] }, { "cell_type": "code", "execution_count": 37, "id": "fab6f1ed-543f-4f42-b1d5-2551742e3a4f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 5.2: .0001 seconds, answer 369761800782619 correct" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(5.2, 369761800782619, lambda:\n", " count_fresh_ids(fresh_ranges))" ] }, { "cell_type": "markdown", "id": "6b83e353-3b77-4645-85b9-2f6ee6ff9e1d", "metadata": {}, "source": [ "# [Day 6](https://adventofcode.com/2025/day/5): Trash Compactor\n", "\n", "Trash Compactor? [I've got a bad feeling about this!](https://youtu.be/CZgeYSqUeTA?si=5UPS_HiCOmTKrEWX&t=32) We've fallen into a garbage smasher and have been asked to help some of the resident cephalopods children with their math homework. We can parse the homework worksheet, but we were told that the exact alignment of columns matters, so I'll keep each line as a string rather than converting it to a list of ints.\n", "\n", "\"Gary" ] }, { "cell_type": "code", "execution_count": 38, "id": "bca852a9-e4c5-4706-abfc-afc6d4a4eeb5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Puzzle input ➜ 5 strs of size 3732:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", " 4 82 68 85 74 6 56 14 2 8669 66 13 927 3 235 44 52 16 37 61 82 1774 96 15 775 789 91 ...\n", " 6 87 39 72 56 12 69 79 58 4378 86 49 146 5 412 85 7751 577 69 813 55 9942 753 49 734 587 15 ...\n", " 827 446 82 72 76 21 31 32 96 3257 21 21 171 2 31 17 9178 977 11 469 58 712 162 4 1 132 91 ...\n", "9472 154 36 76 5 89 37 5 28 6 95 49 82 66 7 44 8183 524 38 819 11 7 825 9 8 397 48 ...\n", "+ + + * * * + * * + * + * * + + + + * + * + * + * * * ...\n" ] } ], "source": [ "worksheet = parse(6, str)" ] }, { "cell_type": "markdown", "id": "ae8a7f1d-07ec-46e4-880f-abbd82d46a67", "metadata": {}, "source": [ "### Part 1: What is the grand total of the answers to the individual problems?\n", "\n", "We humans are used to arithmetic problems written in left-to-right order, but cephalopods use top-to-bottom order, with a postfix operator in the last row. We need to compute the sum or product for each column and add all those results together. So the problem in the first column above would be \"`4 + 6 + 827 + 9472`\". Here's the code:" ] }, { "cell_type": "code", "execution_count": 39, "id": "92f320f4-c7a3-4dfd-ae61-6b1b180bdc93", "metadata": {}, "outputs": [], "source": [ "def grand_total(worksheet):\n", " \"\"\"The sum of the individual sum/product problems, where each column is a problem.\"\"\"\n", " columns = T(map(str.split, worksheet)) # Columns are the transpose of the rows; `T` is transpose\n", " operations = {'*': prod, '+': sum}\n", " return sum(operations[op](mapt(int, numbers)) \n", " for (*numbers, op) in columns)" ] }, { "cell_type": "code", "execution_count": 40, "id": "92a47f3a-127f-41e8-bee1-6276885bd36b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 6.1: .0015 seconds, answer 5877594983578 correct" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(6.1, 5877594983578, lambda:\n", " grand_total(worksheet))" ] }, { "cell_type": "markdown", "id": "226772ae-0d6e-43b8-9159-171ec1b36a5d", "metadata": {}, "source": [ "### Part 2: What is the grand total of the answers to the individual problems with the new rules?\n", "\n", "We learn that we did all the problems wrong. Cephalopodish number notation is different; numbers are read vertically rather than horizontally and the exact column alignment of each digit matters. Given the worksheet:\n", "\n", " 4 82 68 85 74 6 56 14 2 8669 66 13 927 3 235 44 \n", " 6 87 39 72 56 12 69 79 58 4378 86 49 146 5 412 85 \n", " 827 446 82 72 76 21 31 32 96 3257 21 21 171 2 31 17 \n", " 9472 154 36 76 5 89 37 5 28 6 95 49 82 66 7 44 \n", " + + + * * * + * * + * + * * + + \n", "\n", "The problem in the leftmost column is not \"`4 + 6 + 827 + 9472`\"; rather it is \"`9 + 84 + 27 + 4672`\".\n", "\n", "That means I can't just split each line into numbers, I'll have to be careful to maintain the blank spaces to the right and left of the digits, and I have to know in what position each column starts and ends. That part was tricky, so here's an explanation:\n", "- I note from the worksheet above that each column starts at a position above a `+` or `*` sign.\n", "- Each column ends one character befpre the next `+` or `*` sign (one character is a blank space to separate columns).\n", "- For the last column there is no terminator, so I'll add the string `' *'` to the operator line before computing the start positions.\n", "\n", "In `grand_total2` I first break each line into columns, take the transpose of that (to give a list of problems), do the math on each problem, and return the sum of the results. Within `cephalopodish_math` I call `vertically`, whioch again does a transpose and then puts the digits together into an integer." ] }, { "cell_type": "code", "execution_count": 41, "id": "5866583b-245d-4a43-a037-229bf35f1be2", "metadata": {}, "outputs": [], "source": [ "def grand_total2(worksheet: List[str]):\n", " \"\"\"Solve the problem in each column with cephalopodish math and return the sum.\"\"\"\n", " problems = T(break_into_columns(worksheet))\n", " return sum(map(cephalopodish_math, problems))\n", "\n", "def break_into_columns(worksheet: List[str]) -> List[List[str]]:\n", " \"\"\"Break a whole worksheet into columns by finding the `blanks` (the columns with\n", " only blank spaces) and then separating each line at these posisitons.\"\"\"\n", " *number_lines, operator_line = worksheet\n", " operator_line = operator_line.ljust(len(worksheet[0])) + ' *'\n", " column_starts = [i for i, ch in enumerate(operator_line) if ch != ' ']\n", " return [break_line_into_columns(line, column_starts) for line in worksheet]\n", "\n", "def break_line_into_columns(line: str, column_starts: List[int]) -> List[str]:\n", " \"\"\"Break one line into columns, as specified by the list of `blanks` positions.\"\"\"\n", " return [line[column_starts[i]:column_starts[i + 1]-1] \n", " for i in range(len(column_starts) - 1)]\n", "\n", "def cephalopodish_math(problem) -> int:\n", " \"\"\"Return the sum or product of the vertically-arranged numbers.\"\"\"\n", " *numbers, op = problem\n", " sum_or_prod = (sum if op.strip() == '+' else prod)\n", " return sum_or_prod(vertically(numbers))\n", "\n", "def vertically(numbers: List[str]) -> List[int]:\n", " \"\"\"Return a list of integers found by read numbers vertically by column.\"\"\"\n", " return [int(cat(digits)) for digits in T(numbers)]" ] }, { "cell_type": "code", "execution_count": 42, "id": "39a8fa78-946f-45aa-8d36-76883f4aeaff", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 6.2: .0039 seconds, answer 11159825706149 correct" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(6.2, 11159825706149, lambda:\n", " grand_total2(worksheet))" ] }, { "cell_type": "markdown", "id": "ca461ef3-50c3-4189-b724-5f2b3898f27d", "metadata": {}, "source": [ "I initially had an `IndexError` **bug** because the operator line is shorter then the numbers lines. Then I had an off-by-one **bug** that messed up the problem in the last column. To debug my errors I worked on the smaller example worksheet, doing things like this:" ] }, { "cell_type": "code", "execution_count": 43, "id": "a13dbe89-3178-433f-9a50-28ed9a2f8358", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3263827" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "example = \"\"\"\\\n", "123 328 51 64 \n", " 45 64 387 23 \n", " 6 98 215 314\n", "* + * +\"\"\".splitlines()\n", "\n", "grand_total2(example)" ] }, { "cell_type": "code", "execution_count": 44, "id": "3aa0b661-367a-4316-905a-60f1d9e6df01", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[['123', '328', ' 51', '64 '],\n", " [' 45', '64 ', '387', '23 '],\n", " [' 6', '98 ', '215', '314'],\n", " ['* ', '+ ', '* ', '+']]" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "break_into_columns(example)" ] }, { "cell_type": "code", "execution_count": 45, "id": "13392d9c-fef8-4946-b945-48ad6bc7eca9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[('123', ' 45', ' 6', '* '),\n", " ('328', '64 ', '98 ', '+ '),\n", " (' 51', '387', '215', '* '),\n", " ('64 ', '23 ', '314', '+')]" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T(break_into_columns(example))" ] }, { "cell_type": "code", "execution_count": 46, "id": "e29df77c-7385-4ba9-a27b-4074a78a0d74", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1, 24, 356]" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vertically(('123', \n", " ' 45', \n", " ' 6'))" ] }, { "cell_type": "code", "execution_count": 47, "id": "9a25ff50-f465-4de3-95ca-71b7a3d9569b", "metadata": {}, "outputs": [], "source": [ "assert cephalopodish_math(('123', ' 45', ' 6', '* ')) == 1 * 24 * 356 == 8544" ] }, { "cell_type": "markdown", "id": "953679f2-8b55-4bcb-b46f-db0d7c435ea3", "metadata": {}, "source": [ "# [Day 7](https://adventofcode.com/2025/day/7): Laboratories\n", "\n", "In the teleporter lab is a tachyon manifold in need of repair. We find a diagram of the manifold, with `S` marking the start of the tachyon beams and `^` marking is a splitter. \n", "\n", "I could parse this as a `Grid`, but I think I will just keep it as a list of strings. The main idea of a `Grid` is dealing with the 4 or 8 neighbors; a concept that this problem does not use." ] }, { "cell_type": "code", "execution_count": 48, "id": "e85af831-b6cf-4073-a131-ce68debaea75", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Puzzle input ➜ 142 strs of size 141:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "......................................................................S......................... ...\n", "................................................................................................ ...\n", "......................................................................^......................... ...\n", "................................................................................................ ...\n", ".....................................................................^.^........................ ...\n", "................................................................................................ ...\n", "....................................................................^.^.^....................... ...\n", "................................................................................................ ...\n", "...\n" ] } ], "source": [ "manifold = parse(7)" ] }, { "cell_type": "markdown", "id": "59927e26-3252-4c26-8aef-014afdb6deaf", "metadata": {}, "source": [ "### Part 1: How many times will the beam be split?\n", "\n", "Tachyon beams move downwards unless they enounter a `^` splitter, in which case they split into two beams, one immediately to the left of the splitter and one to the right. We're asked how many splits occur. If two beams end up in the same place they count as one beam, so if that beam is split again, that's just one more split, not two more.\n", "\n", "That suggests I should keep a `set` of current beam positions, and update the set every time we go down one line. (It is a set rather than a list so that duplicate beam positions count as one, not as two. (Also, if I kept a list of positions then given the size of the input there would be quadrillions of beams by the end, so it would take a very long time to get the wrong answer.)) I use the trick of iterating with `for b in list(beams)` rather than `for b in beams` so that I can mutate the set `beams` during the iteration. I also need to keep track of the split count, and return that at the end:" ] }, { "cell_type": "code", "execution_count": 49, "id": "d4d3bdbb-d8b2-4e22-adb4-c99a212a2ca7", "metadata": {}, "outputs": [], "source": [ "def count_splits(manifold: List[str]) -> int:\n", " \"\"\"How many beam split events occur as the beams make their way through the manifold?\"\"\"\n", " start = manifold[0].index('S')\n", " beams = {start}\n", " split_count = 0\n", " for line in manifold:\n", " for b in list(beams):\n", " if line[b] == '^': # Replace the beam position with one on each side and count a split\n", " split_count += 1\n", " beams.remove(b)\n", " beams.update({b - 1, b + 1})\n", " return split_count" ] }, { "cell_type": "code", "execution_count": 50, "id": "0e14ad5e-6871-4a9c-bd94-5a863c2341e0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 7.1: .0007 seconds, answer 1681 correct" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(7.1, 1681, lambda:\n", " count_splits(manifold))" ] }, { "cell_type": "markdown", "id": "7e8174b9-2b66-41ce-9677-807a90b88ec5", "metadata": {}, "source": [ "### Part 2: In total, how many different timelines would a single tachyon particle end up on?\n", "\n", "Now we're told this is a *quantum* tachyon manifold and we need to know how many different *timelines* a single tachyon appears in, or in other words, how many different paths can the tachyon beams take to get to the last line.\n", "\n", "We can't just count the number of beams in the last line, because if a beam in position *b* takes two different paths to get there, that counts as two, not one. Instead, I'll replace the `set` from Part 1 with a `Counter` of `{beam_position: number_of_paths_to_get_here}`. If a beam at position *b* with *n* paths to get there encounters a splitter, then in the next step both positions *b* - 1 and *b* + 1 are incremented by *n*. In the end we return the sum of all the counts of paths." ] }, { "cell_type": "code", "execution_count": 51, "id": "c231059d-edad-4f1c-b584-e811fa8fad46", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 7.2: .0014 seconds, answer 422102272495018 correct" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def count_timelines(manifold: List[str]) -> int:\n", " \"\"\"How many possible paths are there to the final line of the manifold?\"\"\"\n", " start = manifold[0].index('S')\n", " beams = Counter({start: 1})\n", " for line in manifold:\n", " for b, n in list(beams.items()):\n", " if line[b] == '^':\n", " beams[b] -= n\n", " beams[b - 1] += n\n", " beams[b + 1] += n\n", " return sum(beams.values())\n", "\n", "answer(7.2, 422102272495018, lambda:\n", " count_timelines(manifold))" ] }, { "cell_type": "markdown", "id": "135b532d-d9ac-4400-9c6d-3b316d4596e1", "metadata": {}, "source": [ "# [Day 8](https://adventofcode.com/2025/day/8): Playground\n", "\n", "In a giant playground, some elves are setting up an ambitious Christmas light decoration project using small electrical junction boxes. They have a list of the junction box coordinates in 3D space:" ] }, { "cell_type": "code", "execution_count": 52, "id": "a5cc43b2-3c5d-4d28-8c94-112bbb5739e7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Puzzle input ➜ 1000 strs of size 13 to 17:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "83023,97914,59845\n", "95221,6604,47587\n", "15200,13848,533\n", "91106,47235,95124\n", "91396,58746,56994\n", "72070,33359,10785\n", "13733,43410,23707\n", "84853,78378,68689\n", "...\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Parsed representation ➜ 1000 tuples of size 3:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "(83023, 97914, 59845)\n", "(95221, 6604, 47587)\n", "(15200, 13848, 533)\n", "(91106, 47235, 95124)\n", "(91396, 58746, 56994)\n", "(72070, 33359, 10785)\n", "(13733, 43410, 23707)\n", "(84853, 78378, 68689)\n", "...\n" ] } ], "source": [ "boxes = parse(8, ints)" ] }, { "cell_type": "markdown", "id": "ee9f47ae-09f5-479e-9e34-34246d723952", "metadata": {}, "source": [ "\"Gary\n", "\n", "### Part 1: What is the product of the sizes of the three largest circuits?\n", "\n", "The goal is to start connecting junction boxes, starting with the two boxes that are closest to each other in 3D space, then the next two closest, and so on. (I assume that a box can connect to an unlimited number of other boxes.) After connecting the 1000 pairs that are closest together, what do you get if you multiply together the sizes of the three largest circuits?\n", "\n", "I recognize this as a [**greedy algorithm**](https://en.wikipedia.org/wiki/Greedy_algorithm), consuming shortest links first, and I've [done that before](TSP.ipynb). I also recognize this as a [**Union-Find**](https://en.wikipedia.org/wiki/Disjoint-set_data_structure) problem, and I know there are efficient data structures for that problem. However, for this problem we don't make heavy use of the union-find functionality, so keeping it simple seems to be the best approach. (After finishing my code I feel vindicated: I see in my [other notebook](Advent2025-AI.ipynb) that Claude Opus 4.5 implemented a Union-Find data structure, and ended up with code that ran slower than my simpler approach.)\n", "\n", "The function `greedy_connect` will keep a dict that maps each box to the circuit it is part of (initially just itself), and update that dict when two circuits are connected together. Then I'll go through the 1000 `closest_pairs` of boxes, updating the dict for each one, and return the dict at the end. Then the function `largest` will find the largest 3 circuits, and `prod` will multiply the sizes together." ] }, { "cell_type": "code", "execution_count": 53, "id": "fb7744c9-105b-439b-aa57-caf93b8117b8", "metadata": {}, "outputs": [], "source": [ "def greedy_connect(boxes, n=1000) -> Dict[Point, Tuple[Point, ...]]:\n", " \"\"\"Go through the `n` closest pairs of boxes, shortest first. \n", " If two boxes can be connected to form a new circuit, do it.\"\"\"\n", " circuits = {B: (B,) for B in boxes} # A dict of {box: circuit}\n", " for (A, B) in closest_pairs(boxes, n):\n", " if circuits[A] != circuits[B]:\n", " new_circuit = circuits[A] + circuits[B]\n", " for C in new_circuit:\n", " circuits[C] = new_circuit\n", " return circuits\n", "\n", "def closest_pairs(points, n=1000) -> List[Tuple[Point, Point]]:\n", " \"Return the `n` closest pairs of points, sorted shortest first.\"\n", " pairs = combinations(points, 2)\n", " return sorted(pairs, key=lambda link: distance_squared(*link))[:n]\n", "\n", "def largest(n, circuits) -> List[int]: \n", " \"\"\"The lengths of the `n` largest circuits (ones with the most boxes).\"\"\"\n", " return sorted(map(len, set(circuits.values())))[-n:]\n", "\n", "def distance_squared(P: Point, Q: Point) -> float:\n", " \"\"\"The square of the distance between 3D points P and Q.\"\"\"\n", " # Since we only care about sorting by distance, the distance squared is cheaper to compute\n", " return (P[0] - Q[0]) ** 2 + (P[1] - Q[1]) ** 2 + (P[2] - Q[2]) ** 2" ] }, { "cell_type": "code", "execution_count": 54, "id": "337ab7d6-d142-4c56-a0a3-2b6cd06cd895", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 8.1: .6008 seconds, answer 24360 correct" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(8.1, 24360, lambda:\n", " prod(largest(3, greedy_connect(boxes, 1000))))" ] }, { "cell_type": "markdown", "id": "3291fa28-a8fa-4ef8-90b3-2b4b6fc9625e", "metadata": {}, "source": [ "### Part 2: What is the product of the X coordinates of the last two junction boxes connected?\n", "\n", "Now we are asked to connect all the boxes into one circuit, still closest first, and compute the product of the X coordinates of the final pair of boxes to be connected. Unfortunately I don't see a way to make `greedy_connect` do both parts; I'll have to copy and paste most of `greedy_connect` to form `last_connected`, which keeps connecting until all the boxes are connected into one circuit, and then returns the two boxes that made the final connection. " ] }, { "cell_type": "code", "execution_count": 55, "id": "1096ded6-749e-4787-9b90-2de917b147c4", "metadata": {}, "outputs": [], "source": [ "def last_connected(boxes) -> Tuple[Point, Point]:\n", " \"\"\"Go through tall the pairs of boxes, in closest first order. \n", " Return the last two boxes that finally make it all one big circuit.\"\"\"\n", " circuits = {B: (B,) for B in boxes} # A dict of {box: circuit}\n", " for (A, B) in closest_pairs(boxes, len(boxes) ** 2):\n", " if circuits[A] != circuits[B]:\n", " new_circuit = circuits[A] + circuits[B]\n", " if len(new_circuit) == len(boxes):\n", " return (A, B)\n", " for C in new_circuit:\n", " circuits[C] = new_circuit" ] }, { "cell_type": "code", "execution_count": 56, "id": "58f06244-ca67-47c9-8ca5-3346a249e1fc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 8.2: .6149 seconds, answer 2185817796 correct" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(8.2, 2185817796, lambda:\n", " prod(Xs(last_connected(boxes))))" ] }, { "cell_type": "markdown", "id": "fa988909-1a8b-4e8c-aca6-c53af99bc0b6", "metadata": {}, "source": [ "Today's puzzles had the slowest run times yet. I could perhaps make them faster by mutating sets rather than forming a new tuple for each new circuit, but I think gains from that would be small, and since the run time is still under a second, I'll leave the code as is." ] }, { "cell_type": "markdown", "id": "9e75bcf2-d62b-47b1-bec0-b2449351d819", "metadata": {}, "source": [ "# [Day 9](https://adventofcode.com/2025/day/9): Movie Theater \n", "\n", "The Elves are redecorating the movie theater floor by switching out some of the square tiles in the big grid they form. Some of the tiles are red; their coordinates form the day's input file:" ] }, { "cell_type": "code", "execution_count": 57, "id": "2dba6fa4-a09b-4ab3-a163-0f94f98e82f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Puzzle input ➜ 496 strs of size 10 to 11:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "98214,50351\n", "98214,51580\n", "98424,51580\n", "98424,52775\n", "97835,52775\n", "97835,54031\n", "98280,54031\n", "98280,55255\n", "...\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Parsed representation ➜ 496 tuples of size 2:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "(98214, 50351)\n", "(98214, 51580)\n", "(98424, 51580)\n", "(98424, 52775)\n", "(97835, 52775)\n", "(97835, 54031)\n", "(98280, 54031)\n", "(98280, 55255)\n", "...\n" ] } ], "source": [ "red_tiles = parse(9, ints)" ] }, { "cell_type": "markdown", "id": "f8d3b123-234d-41b9-bb5b-090ad1b11e78", "metadata": {}, "source": [ "### Part 1: What is the largest area of any rectangle you can make?\n", "\n", "The Elves would like to find the largest rectangle that uses red tiles for two of its opposite corners. That's easy; we can try all combinations of two corners and take the corners with the maximum area. The only tricky part is remembering that we have to add one to the delta-x and delta-y values before multiplying them; the area of a square with corners (0, 0) and (1, 1) is 4 tiles, not 1." ] }, { "cell_type": "code", "execution_count": 58, "id": "75f2742e-9dbd-4005-a882-3d3931fb1b36", "metadata": {}, "outputs": [], "source": [ "Corners = Tuple[Point, Point] # Type representing a rectangle as specifyied by two corners\n", "\n", "def tile_area(corners: Corners):\n", " \"\"\"Area, in tiles, of a rectangle formed by tiles at these corner positions.\"\"\"\n", " (x1, y1), (x2, y2) = corners\n", " return (abs(x1 - x2) + 1) * (abs(y1 - y2) + 1)\n", "\n", "assert tile_area(((0, 0), (1, 1))) == 4" ] }, { "cell_type": "markdown", "id": "271f2f81-dc40-41db-9912-0c45f4d75dbb", "metadata": {}, "source": [ "That's all there is to Part 1; just maximize the area over all combinations of two corners:" ] }, { "cell_type": "code", "execution_count": 59, "id": "27f350c5-7866-4b7b-8d32-91512fcec5b9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 9.1: .0264 seconds, answer 4772103936 correct" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(9.1, 4772103936, lambda:\n", " max(map(tile_area, combinations(red_tiles, 2))))" ] }, { "cell_type": "markdown", "id": "dbd4e094-109f-420c-90b9-0ada15b1da9d", "metadata": {}, "source": [ "### Part 2: What is the largest area of any rectangle that has only red and green tiles?\n", "\n", "In Part 2 we pay attention to the **green** tiles on the floor. Every red tile is connected to the red tile before and after it (in the input list order) by a straight line of green tiles. (It is guaranteed this will always be a straight horizontal or vertical line.) The first red tile is also connected to the last red tile. This forms a closed polygon, and the interior of the polygon is also all green. (The color of the tiles outside of the polygon is not stated, but I'm saying white.) The elves want to know: What is the largest area of any rectangle that consists of only red and green tiles?\n", "\n", "**This is a tough one!** More difficult than all the previous puzzles. There are only 496 red tiles, so enumerating all pairs of them in Part 1 was easy. But there are roughly 100,0002or 10 billion total tiles, so filling in all the green tiles and checking them for each pair of corners would be too slow. \n", "\n", "To get some ideas for what to try, I really want to see what the red and green tiles look like. I'll plot the border tiles, but not the interior tiles:" ] }, { "cell_type": "code", "execution_count": 60, "id": "b5967a65-338d-4198-9f59-986ff74132e6", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def plot_tiles(red_tiles, figsize=(8, 8)) -> None:\n", " \"\"\"Plot the red-and-green border tiles.\"\"\"\n", " plt.figure(figsize=figsize)\n", " plt.plot(*T(red_tiles), 'g-')\n", " plt.plot(*T(red_tiles), 'r.')\n", "\n", "plot_tiles(red_tiles)" ] }, { "cell_type": "markdown", "id": "ef662323-d014-4c64-88cf-b6e777aee3d8", "metadata": {}, "source": [ "**Very Interesting!** Here's what I'm thinking:\n", "- Most of the lines of green tiles are very short, except for the two long lines across the \"equator.\"\n", "- A red-and-green rectangle can't cross the two equator lines, because there are white tiles between them.\n", "- Therefore it seems that one of the corners of the maximal rectangle has to be one of the two points on the east end of the equator lines, and the other corner has to be somewhere on the left side of the circle, in the same semi-circle as the first corner.\n", "- The points are all roughly in a circle, so we're looking for a rectangle roughly inscribed in the circle.\n", "- A roughly correct way to check if a candidate inscribed rectangle is all red-and-green is to see if it contains a red tile in the interior.\n", "- To be more precise, it would be ok if a red tile is on the border of the rectangle. It would also be ok if the red tile is part of a line that only goes one square in from the border. That would just mean more green on the inside. But if the red tile is two squares in from the border, then there must be a white square on at least one side of it, and thus a white square insiude the rectange. \n", "- This red-tile-in-interior heuristic by itself isn't enough to stop a candidate rectangle from crossing over the long equator lines. Or detect a line that starts on the border or one square in and then crosses all the way across the rectangle. We can fix that by estimating the side-length of the rectangle we are looking for and then altering the set of red tiles by inserting some more red tiles on any lines that are longer than that. Then, any rectangle of sufficient size that crosses a long line will contain a red tile in the interior. \n", "\n", "I'm ready to start coding.\n", "- `find_possible_corners` will return a list of the two candidate corner points at the east end of the equator lines.\n", "- `breadcrumbs` will leave \"breadcrumbs\" (that is, red tiles) along the trail at least every `d` spaces." ] }, { "cell_type": "code", "execution_count": 61, "id": "e08d6c65-5b4e-456e-b4de-38339d209372", "metadata": {}, "outputs": [], "source": [ "def find_possible_corners(red_tiles) -> List[Point]:\n", " \"\"\"Split the tiles into top and bottom halves, and also return the two right-side corners.\"\"\"\n", " # Find the index, i, of the tile with the biggest gap to the next tile\n", " i = max(range(-1, len(red_tiles) - 1), key=lambda i: distance(red_tiles[i], red_tiles[i + 1]))\n", " return red_tiles[i+1:i+3]\n", " \n", "def breadcrumbs(points, d=10000) -> List[Point]:\n", " \"\"\"Leave extra points along the trail on long lines, every `d` spaces.\"\"\"\n", " trail = [points[-1]]\n", " for p in points:\n", " while distance(trail[-1], p) > d: \n", " q = trail[-1]\n", " dx, dy = sign(X_(p) - X_(q)), sign(Y_(p) - Y_(q))\n", " trail.append((X_(q) + d * dx, Y_(q) + d * dy)) # Leave a breadcrumb\n", " trail.append(p)\n", " return trail" ] }, { "cell_type": "markdown", "id": "4425bb14-d9ca-4afb-8f1c-5787bf3e17a4", "metadata": {}, "source": [ "Let's visualize that these two functions work as intended:" ] }, { "cell_type": "code", "execution_count": 62, "id": "9dabf8bd-bdac-4b9a-941f-9de68480ca5d", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_tiles(breadcrumbs(red_tiles))\n", "plt.plot(*T(find_possible_corners(red_tiles)), 'bD');" ] }, { "cell_type": "markdown", "id": "d8039a9d-1af7-4a74-80c9-18bba48aeb7b", "metadata": {}, "source": [ "Now I'll define `biggest_rectangle` to find the largest possible all-red-and-green rectangle. I'll do that by considering pairs of corner points, where one of the corners can be any red tile, and the other corner by default will be one of the two `find_possible_corners` points. We then sort the possible rectangles by area, biggest first, and go through them one at a time. When we find one that does not have `any_intrusions`, we return it; it must be the biggest.\n", "\n", "The function `any_intrusions` checks to see if a red tile is completely inside the rectangle defined by the corners. " ] }, { "cell_type": "code", "execution_count": 63, "id": "b699b2aa-17c2-416c-bc1c-90110b64dab2", "metadata": {}, "outputs": [], "source": [ "def biggest_rectangle(red_tiles, d=10000) -> Corners:\n", " \"\"\"Find the biggest rectangle that stays within the interior-and-border of the tiles.\n", " If no list of candidates for `corner1_list` are given, use find_possible_corners(red_tiles).\"\"\"\n", " tiles = breadcrumbs(red_tiles, d)\n", " corners_list = combinations(red_tiles, 2)\n", " for corners in sorted(corners_list, key=tile_area, reverse=True):\n", " if not any_intrusions(tiles, corners):\n", " return corners" ] }, { "cell_type": "code", "execution_count": 64, "id": "922d721e-5330-466b-8a54-8a273522c44d", "metadata": {}, "outputs": [], "source": [ "def biggest_rectangle(red_tiles, corner1_list=None, d=10000) -> Corners:\n", " \"\"\"Find the biggest rectangle that stays within the interior-and-border of the tiles.\n", " By default, try `find_possible_corners(red_tiles)` to narrow down choices for first corner.\"\"\"\n", " tiles = breadcrumbs(red_tiles, d)\n", " # Use a given list for first corner, or try to find 2 on equator, or just use all the red tiles\n", " corner1_list = corner1_list or find_possible_corners(red_tiles) or red_tiles\n", " corners_list = list(cross_product(red_tiles, corner1_list))\n", " for corners in sorted(corners_list, key=tile_area, reverse=True):\n", " if not any_intrusions(tiles, corners):\n", " return corners\n", "\n", "def any_intrusions(red_tiles: List[Point], corners: Corners) -> bool:\n", " \"\"\"Does any point p in tiles intrude inside the rectangle defined by the corners?\"\"\"\n", " # OK for a red tile to be on border or just one square in, but not 2 squares in\n", " xrange = range(min(Xs(corners)) + 2, max(Xs(corners)) - 2 + 1)\n", " yrange = range(min(Ys(corners)) + 2, max(Ys(corners)) - 2 + 1)\n", " return any(X_(p) in xrange and Y_(p) in yrange\n", " for p in red_tiles)" ] }, { "cell_type": "markdown", "id": "683f5366-8c80-445f-813f-1b894871a295", "metadata": {}, "source": [ "We're ready to solve the puzzle:" ] }, { "cell_type": "code", "execution_count": 65, "id": "7ff60bbf-9cb6-4102-8b1c-5ef72be03c92", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 9.2: .0296 seconds, answer 1529675217 correct" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(9.2, 1529675217, lambda:\n", " tile_area(biggest_rectangle(red_tiles)))" ] }, { "cell_type": "markdown", "id": "53ef7a00-aef7-4c20-8a2b-d735df8f28dd", "metadata": {}, "source": [ "Let's see what the biggest rectangle looks like, a little bit larger to see more detail:" ] }, { "cell_type": "code", "execution_count": 66, "id": "8ba7df82-cef0-4c94-8ffa-1822910d21f7", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA/QAAAPHCAYAAACGywJhAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAA9hAAAPYQGoP6dpAADJ9klEQVR4nOzdf3zb5X3v/fdXcpz4B9HS0ZDFAkGwEkLp2g5SCilg0hZvhdIfB9oVSA01cZa40BRoC92asd0rGbSD7CR1Z4NOEtJ0jNKb3VubMljrpqWUEnKarWloMGck5Gug9MypjBXHsq3r/uOyZeuHLTmWLEt6PR8Pgfz1Zekb2Zb10XVd749jjDECAAAAAABFxVPoEwAAAAAAAFNHQQ8AAAAAQBGioAcAAAAAoAhR0AMAAAAAUIQo6AEAAAAAKEIU9AAAAAAAFCEKegAAAAAAilBFoU9gtovFYnr11Vd1yimnyHGcQp8OAAAAAKDEGWP05ptvavHixfJ4Jp6Hp6DP4NVXX9Xpp59e6NMAAAAAAJSZo0ePyu/3T/h5CvoMTjnlFEn2gZw/f36BzwYAAAAAUOp6e3t1+umnx+vRiVDQZzC6zH7+/PkU9AAAAACAGZNp2zeheAAAAAAAFCEKegAAAAAAihAFPQAAAAAARYiCHgAAAACAIkRBDwAAAABAEaKgBwAAAACgCFHQAwAAAABQhCjoAQAAAAAoQhT0AAAAAAAUIQp6AAAAAACKEAU9AAAAAABFiIIeAAAAAIAiREEPAAAAAEARoqAHAAAAAKAIUdADAAAAAFCEKOgBAAAAAChCFPQAAAAAABQhCnoAAAAAAIoQBT0AAAAAAEWIgh4AAAAAgCJEQQ8AAAAAQBGioAcAAAAAoAhNuaD/8Y9/rA996ENavHixHMfRP//zPyd83hiju+++W4sXL1ZVVZUaGhr0q1/9KmHMwMCAbrnlFp166qmqqanR1VdfLdd1E8YcO3ZMq1evls/nk8/n0+rVq/W73/0uYcwrr7yiD33oQ6qpqdGpp56qW2+9VdFoNGHML3/5S1122WWqqqpSXV2d/vqv/1rGmKn+swEAAAAAmFWmXNBHIhG94x3v0NatW9N+/r777tP999+vrVu3au/evVq0aJE+8IEP6M0334yP2bBhgx5//HE98sgjevrpp9XX16errrpKw8PD8THXXXed9u/fryeeeEJPPPGE9u/fr9WrV8c/Pzw8rCuvvFKRSERPP/20HnnkEX3nO9/R7bffHh/T29urD3zgA1q8eLH27t2rLVu26Gtf+5ruv//+qf6zAQAAAACYVRwzjelqx3H0+OOP6yMf+YgkOzu/ePFibdiwQV/84hcl2dn40047Tffee6/Wrl2rcDist771rdq5c6c+8YlPSJJeffVVnX766dq9e7caGxv1wgsv6Nxzz9Wzzz6rCy+8UJL07LPP6qKLLtKvf/1rLVu2TN///vd11VVX6ejRo1q8eLEk6ZFHHtGNN96oN954Q/Pnz9c3vvEN3XXXXfrNb36juXPnSpL+9m//Vlu2bJHrunIcJ+XfNDAwoIGBgfjHvb29Ov300xUOhzV//vyTfagAAAAAAMhKb2+vfD5fxjo0p3voX375Zb3++uu64oor4sfmzp2ryy67TM8884wkad++fRocHEwYs3jxYp133nnxMT/72c/k8/nixbwkvec975HP50sYc95558WLeUlqbGzUwMCA9u3bFx9z2WWXxYv50TGvvvqqDh8+nPbfsGnTpvgyf5/Pp9NPP32ajwoAAAAAALmX04L+9ddflySddtppCcdPO+20+Odef/11VVZWasGCBZOOWbhwYcrtL1y4MGFM8v0sWLBAlZWVk44Z/Xh0TLK77rpL4XA4fjl69GjmfzgAAAAAADOsIh83mryU3RiTdnn7ZGPSjc/FmNEdBhOdz9y5cxNm9AEAAAAAmI1yOkO/aNEiSamz32+88UZ8ZnzRokWKRqM6duzYpGN+85vfpNz+b3/724Qxyfdz7NgxDQ4OTjrmjTfekJS6igAAAAAAgGKS04L+rLPO0qJFi/TUU0/Fj0WjUe3Zs0cXX3yxJOn888/XnDlzEsa89tprOnDgQHzMRRddpHA4rOeeey4+5uc//7nC4XDCmAMHDui1116Lj3nyySc1d+5cnX/++fExP/7xjxNa2T355JNavHixzjzzzFz+0wEAAAAAmFFTLuj7+vq0f/9+7d+/X5INwtu/f79eeeUVOY6jDRs26J577tHjjz+uAwcO6MYbb1R1dbWuu+46SZLP51Nzc7Nuv/12/eAHP9AvfvEL3XDDDXr729+u97///ZKk5cuX64//+I+1Zs0aPfvss3r22We1Zs0aXXXVVVq2bJkk6YorrtC5556r1atX6xe/+IV+8IMf6I477tCaNWviKYDXXXed5s6dqxtvvFEHDhzQ448/rnvuuUe33XZbxi0AAAAAAADMZlPeQ//888/r8ssvj3982223SZKampq0fft2feELX1B/f7/Wr1+vY8eO6cILL9STTz6pU045Jf41DzzwgCoqKvTxj39c/f39et/73qft27fL6/XGx+zatUu33nprPA3/6quv1tatW+Of93q9+t73vqf169dr5cqVqqqq0nXXXaevfe1r8TE+n09PPfWUWltbdcEFF2jBggW67bbb4ucMAAAAAECxmlYf+nKQbf8/AAAAAAByoSB96AEAAAAAwMygoAcAAAAAoAhR0AMAAAAAUIQo6AEAwORcV+rstP/P5VgAADAtFPQAAGBioZBMICCtWiUTCGigvU2RaCTtZaC9LT5WgYAUCk18u7xJAADAtJFynwEp9wCAouK6UleXFAxKfv/0xrmuTCAgJxaLHxpypDM3SN2+xKF1YenIZsk7/lWF1ysdPpx6+6GQzJo1coyRcRxFv7FVQzc1pT2Fim07VLn+FnsOHo/U0SE1N0/87wIAoARkW4dOuQ89AACYpUIhmZYWObGYjMejaNuWtIVy1kVyV1dCMS9JFUaq70kt6IM9ScW8JA0Pq/+FXyq2cEH8kON2q2qkmJckxxhV/Fmrzj7UOuGbBM7o7cZi0tq1UmPj5G9WAABQJpihz4AZegBAUchyNn1KM+lpbtN4vep/8aCMvy5hqGfvPs1772Vyxh0zkt59s/T8uJu95oD07cdST//aa6THzks81vCy1Lkjzb+1s1NqaEg9nu3qBAAAZjlm6AEAKCdZzqZPNJOul15KLYL9fkXbtsj7Z62qkGQ8Hjnt7apesjT1/qPDKYccSTWDqcfS2fnRh7X9mo8ljnW7ZR4+Jz6br5Fz6D9jsUw0kvhvZWk+AKAMUdADAFAKgkFbcCfNpu/emDibPpUiWZKGhwdU48hOt2e4f3k8dll8pvv/TuL9y+PRvEsvlyprEm+zsjrlbmOxmJZuXZZ21QFL8wEA5YaCHgCAUjA6m76uVRXGFtNpZ9OzLJKl1OX5zmSFst9vZ8XXrrUz/hPd/5Kl0oMPJoxTe3v6wrurK7Hwl+TVNFcd5FMuAwkBAMgCBT0AACVi6KYmnX2oVfU90u6NB9Mvjc+ySJZOolBubrbF/ksvSfX1Exer2Y6byqz/zuWJWw68XnvbE8l18Z1lcj9bAwAAuUQoXgaE4gFAiZrKLOnevdJPfiJdcom0YkXubjfHYyPRiGo31UqS+u7qU03yEvbR2wkEUorkdEF3jtutqmCaQjldgF6+hEKps/lpCuDBT92gip27NLo7YGj19Yo+1J72JrMuqrPsGuC43aqqT9xGMCwp8LlpBBICAMoaoXgAAEwky0JNkipvXpv7QnH0HPLQi70ubGfWHbfbLm9Plu3SeMl+fdLYCZfH50s2s/muq4pd/xgP3HMkOd/cpWWn7jr5VniuG/8Zkex2A++69O31rjkgfTtpesQr6aKj0mOzcWsAAKBkMEOfATP0AFBismzvJkkXuNJzDyljKzbJFoqvPCB5xo/1eNTf9UL6me8sZnSnervDD3Wo5jO3yWtGEukne0PBdTMveT+ZsYXQ2SmtWpVyuKFJ2nNW0rEJWuH1P7lbscsujX/s+dEeVTVemdVtXntAejRNK74Tux7W8Ljk/lmx4gEAUBSYoQcAIJ0s27tJ0ntfSW2z5khaeTS1oL/4aGLRLdlZ3aYvLkvpr57tjO5UbndKAXaSPZZtETmVsYWQ5V57SfLs3Sez47KUN2kuffSDev6ZsWMXuNJzSn0z5/tr9ii24vyE28w6uX/JUg2MDy4caQNIgB4A4GRR0AMAykuW7d2kkeLvydTib9OX9+grSUWd59vfkR5Lv2Q+2VR6sWd7u2W9nHsq2wiiwymHHEk1g4nHagfTv5lTNRhLba83leR+jVvub4wGhgY0lKZdoDTFLRwU/gBQllhynwFL7gGg9Ay0t6W0d5uwULrxRmnHuDXaTU3S9u2p41xXOuMMaXx/d8dR/0u/zmrJvTwe6ciR1GIsy9tlObey2xqQZSjgST2eme5/Cts9prLVguR8ACg92dahyav4AAAoeUM3NenMDXY/dP+LBycvfrZvl557TnrgAfv/dMW8ZAu4Bx+0BZUkeTxyHnxQ1UuWqqayJuFSvWSpnAcftAWiZP/f0THx0vgsbrd6yVK7Z378bc50gF2h+f1SQ8Pk/+bR2fxxj9PobP60H89M9z/Jdo9kk221qN1UG78su7NWFetax253dKuF6058ngCAksEMfQbM0APALJHDFm9ZtXebznnmI2wu27GzPcButijE4zmFloGeb39HVTekbrW49holZCdMFPKnzk775gIAoChlW4dS0GdAQQ8As8AU2sxls/w4Eo1o2Z21CvZI39t4KP1eayAfQqHUvfbpVojkc6vF3r3ST34iXXKJtGLFxOfKvnwAKBgK+hyhoAeAAsvDvuMptXcDci3bWf9QSGppsTP6k+yNH/zUDarYuUuObGjj0OrrFX2oPe1NVt68Nqux7MsHgMKioM8RCnoAKLAp9BifqB/4+GXKye3dJJVfeByKRw6D9i5wpeceSm3F9+6bE9swntTvCLP5AJBT9KEHAJSGqbSZy6LFW1m3d0Px8fsn/7mcJGgvuaB/7yvpW/GtPJpY0E/0O9L/wi8VW7gg5RSYzQeAwmGGPgNm6AGg8LJuM5fFvmPau6GkTCVob+8+zXvvZSkz9Cee3qPYivMzjkueyZdOYjafmXwAyApt6wAAJSPrNnNZtHijvRtKSpZt+Goqa1S18lI5TYkrWJymJlWtvDRxXHQ47Ux+zWDq3U82mx+JRhIuA+1tMoGA3UITCNiMAADAtDBDnwEz9ABQeFNuM5dN6Bjt3VBKpvLzvHev9NOfSitXpk+5z8Gsf0725QNAGWMPPQCgsKaytDaLNlp1YTsb6LjdUqY2c5n2HWc7BigWU/l5XrFi8nZ1o7P+49rrjc76p4gOpxxKN5s/5ewKluYDQFaYoc+AGXoAOAlT6BufTRst2swBBZDtSpcsZvMdt1tV9efIGZ9vkaalpETIHgBItK3LGQp6AEiSaeYsx220WKoLzHKhUMJsvtKFVrquzBlnJBT0w5ICn0t8XpjS7zuz+ABKGKF4AIDcC4XioVYmENBAe1tK8FX/wf+csI1WssnaaI2adKkugMJrbrYFd2en/X+62fSuroRiXpK8Sn1eyDZkj4A9ALCYoc+AGXoAGJHlzPtEs+7JrbGk7Npo0WYOKAFZLs3PJmSPVTsAygEz9ACAqXFdO8Pmuuk/39WV1cx77WD6WfeqwdhJtdGizRxQArJsr5dNyzxW7QDAGGboM2CGHkBZyCLELm2oleOo/6Vfp4ZfTXVGPVMbLYk2c0ApyPR7nMVMPqt2AJQDQvFyhIIeQMnLcil9XVh65YGkpV0ej3TkSOqL6GxCsgAgnSyePwba2+Rd16oKYwt+h+cYACWGPvQAgOxSoCdZSj++oA/2pNmnFYul7yPd3Cw1NjKjDmDqsnj+GLqpSe99vlUrj0qbvvxDVa28NP1tkYQPoMQxQ58BM/QAilaWveDzupQeAPJgoL1NFeta5TWa8PmNfvYAihlL7nOEgh5AUZpCL3iW0gMoKlk8v5GED6DYkXIPAOUsy0R6KcNS+mTZ9JsGgHzK4vmNJHwA5YI99ABQioJBGY8n4UWv8Xq1e2Niz2fJLqU3O9Mspa+vT3/bfj8zXAAKJxi0q4gmeX6b8vMaABQpZugBoBT5/XZP6UhDZzNBz2f6vAMoOln0tK9esjTlOZDnNQCliD30GbCHHkCxikQjWnZnrep7pN0bD6l6ydLJv4A+7wCKSYbnrCk/B47eZjap+KTnA8gz2tYBANTts5fkZfZpsZQeQDHJ8jnLyfb2QiGZNWvkGCPjOIp+Y2vaziCk5wOYTSjoAQAAUHIqtu2IJ92bncs1MEHrTmmkLedIMS9JjjGq+LNWnX2oNaEzyGh6vjO6vjUWs50/Ght5QxRAQVDQAwAAoLS4rp1FHym8nVhM3nWpBfqoaw5I307ahOqVdNFR6bFx4ydNz6egB1AAFPQAUOwm2ctZF7YvQB23W8pm/ygAlIJJWtulK+gnWpa/86MPa/s1HxsbR3o+gFmGgh4AilkoJNPSIicWk/F4bKrzyJLS4Yc6Epabss8TQNnIorXdeI7bLfOdc+JL7iVJHo/mXXq5VFkzdmzJUg20bZF3XasqjGx70PHp+YTlAZhhtK0DgGLluvFiXhpbUrrszlotu7NWNZ+5Lb401Bnd5+m6BTxhAJghWbS2S2nf+eCDie07OzomLMrje+iN0cDQgCLRiAba22QCAWnVKikQkEKh/P87AZQ92tZlQNs6AAWRzSxPZ6d94ZikockuH+3cMcHXNDTk8kwBYPaaajvOTONdVyYQSFhyP+RIFzVLz4aS9td7vdLhw8zUAzgptK0DgGI1yTL68ZxAnaocJ2GJqHEc7d74a3udfZ4Ayt1U23FmGj/B3vyVRwnLA1AYFPQAMJtMsIw+XTJzXVh6xSSGOTmOo+rK6rHlpmvX2heVXq80fp8nAGDqJtibv+nLP5R56nLeRAUw49hDDwCzySTJzMmCPWmexGMxOyMk2QC8w4ftMvvDhwnEA4DpmmBvftXKS+1qqpF3WA1vogKYIeyhz4A99ABybrL98Wn2ZxqvV/0vpiYzO263qoJpltWzZxMA8ivNXvtINKJld9aqvkfavfGQqmkVCmAasq1DmaEHgJkUCsVTkE0goIH2NkWikbHLwgU68clrFA9QluTccEPaZObqJUvlJM0UMSMEADPA77cBo0nPt90+ac9ZStsaDwDygRn6DJihB5AzE6Qjn7lB8f3xdWHFe8fHZZp1n2qKMwAg5yLRiGo31UqS+u7qU834/vUAMEXM0APAbJPF/vhgzyRJyROZYKYIAFAEXNdmnbhubsYBKCuk3APATAkGZTyelP3xuzeO7Y933G7azQFAkaoL2zdmHbdbymYPfSgks2aNHGNkHEfRb2xN26a0YtsOVa6/xf5t8HhsMB9BpwDEkvuMWHIPIJcG2tvkXdeqCmOLeae9PfVFWSiU2m6OF24AMKsNtLepYl2rvEYyHo9NvU9TnI9y3G5V1Z8jZ9xL8WFJgc8poU3pSW3FAlD0sq1DKegzoKAHMCWTJdjL7rFsaK3VylekTRv3qGrlpRPfDvviAaA4ZJGRkuyaA9K3H0s9fu010mPnjX3c8LLUuSPNDXR22u1WAEpStnUoS+4BIFdCIZmWFjmx2ISzM8MPdejZkJ1pMf9++cTLJv1+CnkAKBaTZKRMVNA7E9zUzo8+rO3XfGxsXKatWBneSAZQ2pihz4AZegBZyVeCPQBg9nNdKRCQkjJS+l88OGELu3RL7uXxSEeOpPxNGPzUDarYuUuObDvTodXXK/pQO3vrgRJGyj0AzKR8JdgDAGY/v98W016v/XgkI6V6yVLVVNakvVQvWSrnwQcTvkYdHalv8LquKnb9Y3xG35HkfHOXGlprVbGudexvTyxm81dIwQfKCkvuASAbmZY0kmAPAOWtuVlqbJxa/kk2XzPBG8Yrj07yJjGrvoCywQw9AGQSCskEAtKqVTKBgAba2xSJRhIvCxfoxCev0ehrKyPJueGGhNmZ6iVL5STN4Ki9nRdeAFAq/H4bVDeV5/VMXxMM2uX04xivV5u+vEcm6ThvEgPlhz30GbCHHihzWSYXT2l/PAn2AICpmKCdaVatUAEUJVLuASAXskwunnR/fHLRToI9AGAqJliaP3RTk84+1Kr6Hmn3xoOqXrK0wCcKYKZR0AMobznYGy+xPx4AkGcTvBnc7bOXidL0AZQ29tADKF852hvP/ngAAAAUAnvoM2APPVCi8rE3fuR22R8PAJgJkWhEtZtqJUl9d/WpprKmwGcEIFfoQw8Ak8mib7x0Er3jTybhGACAk1QXlhpetlu/JuW6UmcnfeqBEsMeegClib3xAIASV7FtR3wVmdm5XANtWzR0U1PacZXrb7F/yzweqaODNHygRLDkPgOW3ANFKBSSaWmRE4vJeDyKTvACx/PpT2verkflaGRvfFOTtH172ttL1y4IAICCydfWMQCzQrZ1KAV9BhT0QJFhbzwAoBx0dkqrVqUcbmiS9pw17uOXpc4dE3x9Q0PeTg/A9NCHHkB5ykffeIne8QCA2SUYtMvn2ToGlDUKegClhb3xAIBy4PfbvfDjtoQ57e2qXrI0cdySpRpo2yLvulZVGNm/kZO1Vc2UQQNgViHlHkDxmSyp1++3e+ZHPhx94ULfeABAyWlutlvFOjvt/yfJd3FGV6UZo4GhAUWikZTLQHubTCBgl/IHAjZDBsCsxgw9gOKSReDd8PCAakaT7ibT3Cw1NrI3HgBQvDJtCXNdm3A/8qFjjLzrWnX2oda02TLxwj8Ws7P/jY38fQRmMQp6AMXDdePFvCQ5sVjKi5LksDsn0wsS9sYDAEpZvrJlAMwKFPQAikcWL0p4QQIAwDiE5wEljT30AIrHSODdePZFySH13dWnvrv69L2Nh1LG8IIEAFC2RsPzxmXGTJQtE23boqGRtfnG45k8W2ayPBsAM4aCHkDxGA28G32xkeZFCWF3AAAkITwPKFmOMSZTbFRZ6+3tlc/nUzgc1vz58wt9OkDZi0QjWnZnrep7pN0bD6W25xnluoTdAQCQLdeVCQQSltwPOdKZG5Q2PC9he5vXa98o4O8tkDPZ1qHsoQdQdLp99jJ+718Kwu4AAMge4XlAUaKgBzD7uK7U1WWDfNK8OKgL2xcUjtstTTRDDwAAspeL8LwMf78B5B576AHMLqFQfF+eCQQ00N6WsG9v+KEOHdksde6QqoLL2bcHAEAuTCE8b+j6Tyq+1V7S4HV/qoHv/Qv76oECYA99BuyhB2ZQhv177NsDACDPMmXQTPC32jGSd/w4/j4D05JtHcoMPYDZY5L9e1KGfXsAAGD6/H6poWHiQnyCv9Xe5HH8fQZmBHvoAcweI33mnQn27026bw8AAORfur32Ho9kjJzxC3/5+wzMCGboAcws17V9cF039XOjfeZHPjQeT8L+PXrMAwBQYOn22nd0KPqNrRpy7CHD32dgxjBDD2DmhEIyLS1yYjEZj8cW7zc1JQwZHh5QjSNponSP5mapsZEe8wAAFEqav8VD0YjOPtSq+h5p98aDqqYLDTAjCMXLgFA8IEcyBN5JhN4BAFCsItGIajfVSpL67upTTWVNgc8IKG6E4gGYXTIE3kmE3gEAAABTwZJ7ADMjQ+CdJELvAAAAgClghh7AzBgNvBsXmDM+8I7QOwAAAGBqmKEHMGOGbmrKHJhD6B0AAEWpLmy3zzlut5Tub7zrSl1dtvUdf9+BnKCgBzCjun32MrrMPi2/nz/0AAAUkYptO+LBtmbncg0kdbKp2LZDletvsdvqPB7b+q65uXAnDJQICnoAAAAAJ891bbE+EmzrxGLyrmvV2Yda1e0b62Iz+nnFYtLatXZFHm/gA9PCHnoAAAAAJy9DJxu62AD5www9gPyYYJ9cxv11AACguASDdhn9BJ1s6GID5A8z9AByLxSSCQSkVatkAgENtLcpEo1o+KEOHdksde6QqoLLpVCo0GcKAACmy++3e+LHdakZ38mmesnSlE43dLEBcsMxxiQvgME4vb298vl8CofDmj9/fqFPB5j9XFcmEEh4F37IkS5qlp4NJS2583qlw4f5gw4AQClw3Qm71ESiETW01mrlUWnTl/eoauWlqV9LAj4Ql20dygw9gNyaYB/dyqPsnwMAoKT5/VJDQ9qCvGLbDj0bkjb/mzTv0svjq/ci0YgG2tviK/sUCLCCD5gCZugzYIYemKI0M/TG69WJPT/UvEsvT90/xww9AAClbYLVe2dusNdH293F8foAYIYeQIH4/Sn75Jz2dlWtvFRO0v469s8BAFAGJknBJwEfmB5m6DNghh6Yukg0omV31qq+R9q98ZCqx6fZT7K/DgAAlCDXtUvpk1bv9b94UJINymUFH5CIGXoA+eW6Umen/f8EnHQHJ9lfBwAAStAkKfgk4APTwwx9BszQA2mEQjItLXJiMRmPx/4hvqkp/unhhzpU85nb5DWS8XjsUvvm5gKeMAAAKLgJVulNurIPKFPZ1qEU9BlQ0ANJJgm26fZJdWHCbQAAQPYi0YhqN9VKkvru6lNNZU2BzwgoPJbcA8iPSYJtJMJtAADA1NWFpYaXJcftzjw4i21/QLmoKPQJACgywaBdRp8UbLN740EZf50ct1tmZ5pwm/r6ApwsAACY7Sq27Yiv7jM7l2sgaStf8tjK9bfY1xkej92bz7Y+lDGW3GfAknuUHdeVurqkYHDCJfID7W3y/lmrKjTBHvlQSFq71s7Mj4bb8McWAAAky7CVbzy29aGcsOQewNSFQjKBgLRqlUwgoIH2NkWikZTLwPCAnLQR9iOam+0f185O+3+KeQAAkE6GrXzjsa0PSMUMfQbM0KNsZPkOOe+OAwCAnJmkR73x1yUMddzu7HrWZ7HaEJjtmKEHMCab8Jgs3yHn3XEAAJAzk/Sor6msSbhUL1mqoes/qdGXIUbS4HV/qsjCBWOrCNvb4qsNFQjYbYBACWOGPgNm6FH0MvSMH+W43aqqP0fOuKcE4zjqf+nXCe+QZ/3uOAAAQLYm6FGfPIbWuSgX2dahpNwDpcx148W8JDmxmLzrWnX2oda0QTOvGGn81njHcVRdWS2N7we7ZKl9Jz059I4/lAAA4GT5/ZlfS0yymrDbl2EVIa9TUKIo6IFSluEP33jBnjR7cGKx9H8Em5ulxsbM76QDAADkSjBoW9XROheIo6AHSlmGnvHjTfmPYDbvpAMAAOTK6H77casER/fbS5KWLNVA2xZ517WqwtjXPA6rCFHiCMUDSpnfb/fMj6yjNxmCZpykUBqW0gMAgFklQ2vcoZuadFGztKFROrHnh+lb52YTFgwUCULxMiAUD8UuEo1o2Z21qu+Rdm88NPYu9kSyCaUBAACYhQba21SxrlVeo7RhwBXbdqhy/S12RaLHY2f80xX9QIFlW4dS0GdAQY9iF4lGVLupVpLUd1efasYH3AEAAJQKUvBRQuhDDwAAAKB8TBIGLGVIwQeKFKF4AAAAAIofKfgoQ8zQAwAAACh+oyn44wJ+x4cBVy9ZmhIWTAAwih0z9AAAAABKQ3Oz1Ng4YcDv0E1NOvtQ60hY8MHMYcHALEdBD5Qq17V7yQJ1qgvbfWOO2y3xhwsAAJQyv3/SWfdun70Yf90MnhSQHxT0QCkKhWRaWuTEYqpyHL1i7P4as3M57VkAAEBZm3SiY2RCRMEgS/FRFNhDD5Qa140X85LkGBP/RXdiMWntWvvHCgAAoMxUbNuhI5ulzh1SVXC5BtrbFIlGFIlGNNDeJhMISKtWSYGAFAoV+nSBjOhDnwF96FF0OjvtH6JMYxoaZuR0AAAAZoVJ+tRL9KjH7EIfeqBcBYMynkl+tWnPAgAAytEkferpUY9iRUEPlBq/P7Eli8cjOSMf0J4FAACUq9E+9ePYPvWH9L2Nh1InRJgEQRGgoAdK0NBNTTpzg9TQJPV3vSC98opdZn/4MIF4AACgPE3Sp54e9ShWpNwDxSqLFFZn9EqG9i0AAABlYZI+9fSoRzGioAeK0bi2dMbjse8o39QU//TwQx3xYBda1QEAAIwzyUQHPepRbCjogWKT3JYuFpN3XavOPtSqbp/trTo+pTXeqq6xkVl6AACASUzao348+tVjlmAPPVBsJklolUhpBQAAOBmT9agff6FfPWYT+tBnQB96zDppeqgar1f9Lx6U8dfJcbtVFVyeWPTTRxUAAGBik/So7/aNDUteCSmJ11nIC/rQA8XKdW0iveum//xoW7qRD43HE09oramsUfWSpXKSElxJaQUAAJhEhhWQo1gJidmGPfTAbJIh7G7U8PCAahxJE62vmSTBFQAAAElGe9QnrYDcvfFgQkCe43bL7EyzEpJ+9SgQltxnwJJ7zBiWegEAABROKGSDhIeHx1Y4pukSNNDeJu+6VlWYkZWSo92ECMpDDrHkHig2LPUCAAAonOZmO0HS2Wn/P0nLX2f0tZgxGhgaICgPBcMMfQbM0GPGZAi7G0XoHQAAQIFMsKLSMZJ3/Dhem2GamKEHis1o2J1jPzReb0LY3eiF0DsAAIACmWBFpTd5HKsnMUOYoc+AGXrMpEg0omV31qq+R9q98ZCqlyydeLDrEnoHAAAwk1zXLqkfv6LS45GMkTO+rGKGHtPEDD1QpLp90p6zlLDMPi2/X2po4A8FAADATPH7paSVkk5Hh6Lf2JqwypLVk5gptK0DZlqGBNS6sA2+c9xuabIZegAAAMy8NO2Bh6IRnX2odWSV5cHJV1kCOURBD8ykDH3mhx/qiLekMzuX23eAJ0lYBQAAQAH4/SkTM90+e8m4yhLIIQp6YKa4bryYlyQnFpN3XavOPtSqbl9qf3knFrO9UBsbWbIFAAAAIAV76IGZkqHPPP3lAQAAAEwFM/TATAkGZTyelD7zuzfaPvOO2y2zM01/+fr6ApwsAAAApmLSHKQMGUrAyWKGHpgpGfrM018eAACgOFVs26Ejm6XOHVJVcLkG2tsUiUYUiUY00N4mEwhIq1bZlnehUKFPFyWEPvQZ0IceuZRVn3n6ywMAABQP15UJBBJWWQ450pkb7PXxGUmS6FGPrGRbh7LkHphhGRNQ06SmAgAAYJaaJCfJ0SQZSbzeQw5Q0AMAAADAyQoGJY9HSpOTJImMJOQVe+gBAAAA4GT5/VJSDtJoTlL1kqUpGUpkJCGXmKEHAAAAgOlobpYaG9PmIA3d1KSzD7WOZCgdTJ+hBJwkCnoAAAAAmK5JcpAyZigBJ4mCHpgprivPwf/UBa5UOzhBj1IAAACUnIQe9ZXV9KRHzlDQAzMhFJJpaVFVLKbnZBNPzc7ldr9Vc3Ohzw4AAAB5Mtqj3msk8/A5MpIcY2yQHq8FMU30oc+APvSYtjS9SePoQwoAAFC6JnsdKPFaEBPKtg4l5R7ItzS9SeNG+5ACAACg9Ez2OlDitSCmjYIeyLdgUMYzwa8afUgBAABK12iP+onwWhDTlPOCfmhoSH/xF3+hs846S1VVVVqyZIn++q//WrFx70wZY3T33Xdr8eLFqqqqUkNDg371q18l3M7AwIBuueUWnXrqqaqpqdHVV18t13UTxhw7dkyrV6+Wz+eTz+fT6tWr9bvf/S5hzCuvvKIPfehDqqmp0amnnqpbb71V0Wg01/9sYGJ+f2L/0dHj9CEFAAAobUk96o3Ho+GRT9GTHrmQ84L+3nvv1T/8wz9o69ateuGFF3Tffffpq1/9qrZs2RIfc9999+n+++/X1q1btXfvXi1atEgf+MAH9Oabb8bHbNiwQY8//rgeeeQRPf300+rr69NVV12l4eHh+JjrrrtO+/fv1xNPPKEnnnhC+/fv1+rVq+OfHx4e1pVXXqlIJKKnn35ajzzyiL7zne/o9ttvz/U/G+XOdaXOTvv/NIZuatJFzdKGK6QT/++37djDhwlBAQAAKHXNzfZ1X2en+rteUOBzUkOT1P/iQV4LYtpyHop31VVX6bTTTlMoFIof+x//43+ourpaO3fulDFGixcv1oYNG/TFL35Rkp2NP+2003Tvvfdq7dq1CofDeutb36qdO3fqE5/4hCTp1Vdf1emnn67du3ersbFRL7zwgs4991w9++yzuvDCCyVJzz77rC666CL9+te/1rJly/T9739fV111lY4eParFixdLkh555BHdeOONeuONN7IKuSMUDxmNJNg7sZiMx2Nn429qShgy/FCHaj5zm0039XjkkGgKAABQdiLRiGo31UqS+u7qU01lTYHPCLNVwULx3vve9+oHP/iBXnzxRUnSf/zHf+jpp5/WBz/4QUnSyy+/rNdff11XXHFF/Gvmzp2ryy67TM8884wkad++fRocHEwYs3jxYp133nnxMT/72c/k8/nixbwkvec975HP50sYc95558WLeUlqbGzUwMCA9u3bl/b8BwYG1Nvbm3ABJuS68WJekpxYTN51rVp2Z61qN9nLsjtr48X86BitXTvhbD4AAAAAZCPnfei/+MUvKhwO65xzzpHX69Xw8LC+8pWv6JOf/KQk6fXXX5cknXbaaQlfd9ppp+nIkSPxMZWVlVqwYEHKmNGvf/3117Vw4cKU+1+4cGHCmOT7WbBggSorK+Njkm3atEl/9Vd/NdV/NspVmuTSCiPV90jdPvtxsEfxYj5uNNGUPVMAAAAATlLOC/p/+qd/0je/+U1961vf0tve9jbt379fGzZs0OLFi9XUNLYM2XGchK8zxqQcS5Y8Jt34kxkz3l133aXbbrst/nFvb69OP/30Sc8LZWwkwX58UW+8Xu3eeFDGXydJctxumZ3LEwt/Ek0BAAAATFPOl9x//vOf15133qk//dM/1dvf/natXr1an/vc57Rp0yZJ0qJFiyQpZYb8jTfeiM+mL1q0SNFoVMeOHZt0zG9+85uU+//tb3+bMCb5fo4dO6bBwcGUmftRc+fO1fz58xMuwISSE+y9Xjnt7apeslQ1lTWqqaxR9ZKlds/8SLop6fYAAADlqy4sNbxsJ30SZAhZBtLJeUF//PhxeZJ6LXq93njburPOOkuLFi3SU089Ff98NBrVnj17dPHFF0uSzj//fM2ZMydhzGuvvaYDBw7Ex1x00UUKh8N67rnn4mN+/vOfKxwOJ4w5cOCAXnvttfiYJ598UnPnztX555+f4385ytXQTU06c0OGtNJx6aak2wMAAJSnim07dGSz1LlDqgou10B7myLRiAba22QCAWnVKikQkMYFjAOTyXnK/Y033qh///d/V3t7u972trfpF7/4hVpaWvTpT39a9957ryTb2m7Tpk3atm2bgsGg7rnnHv3oRz/SoUOHdMopp0iS1q1bp+9+97vavn273vKWt+iOO+7Qf//3f2vfvn3yjsx0/smf/IleffVVtbe3S5JaWloUCAT0r//6r5Js27p3vvOdOu200/TVr35VPT09uvHGG/WRj3wkoY3eZEi5RyaklQIAACAj15UJBBK2YQ450kXN0rOhpMwlr9dOArGis2xlW4fmfA/9li1b9OUvf1nr16/XG2+8ocWLF2vt2rXauHFjfMwXvvAF9ff3a/369Tp27JguvPBCPfnkk/FiXpIeeOABVVRU6OMf/7j6+/v1vve9T9u3b48X85K0a9cu3XrrrfE0/Kuvvlpbt26Nf97r9ep73/ue1q9fr5UrV6qqqkrXXXedvva1r+X6nw0AAAAAE5sgTHnlUQKUcfJyPkNfapihRwLXlbq6pGAw/gQbiUa07M5aBXuk7208pOolSwt8kgAAAJh1XNcup08KUz6x54ead+nlqQHKzNCXtYL1oQdKVigU39tkAoH4nqfhhzoS9kKx5wkAAAAp/H4pKSjZaW9X1cpLU0KWCVBGtpihz4AZekhizxMAAAByw3Xtcvr6+pQVn/U90m5WfEIF3EMPlCT2PAEAACAX/P60rxO7ffZi/HUFOCkUK5bcA9kIBmWS2jEar1ebvrwn5bi8XvuOKwAAAJAl+tPjZFDQA9nw+1P2No3ueXKS9kKx5wkAAABTQX96nCz20GfAHnqMmnRvU5q9UAAAAEBGZDUhDfbQA3kw4d6mCfZCAQAAAJMiqwnTwJJ7AAAAACiUYFAiqwkniYIemEiaAJIJw0oAAACAk0F/ekwDe+gzYA99mQqFZFpa5MRiMh6Pom1bNDA8oJrP3CavkYzHY8PwmpsLfaYAAAAoBfSnxzjZ1qEU9BlQ0JehCYJJHCN5x48jlAQAAAB5FIlGVLupVpLUd1efaiprCnxGmCnZ1qEsuQeSTRBM4k0eNxpKAgAAAAAFQEEPJAsGUwJIjMcj4ziJ4wglAQAAQJ5NmuGUJvMJ5YWCHkjm96cEkDgdHXIefDAhrIRQEgAAAORTxbYdOrJZ6twhVQWXa6C9TZFoRJFoRAPtbTKBgLRqlRQISKFQoU8XBcAe+gzYQ1+eJgwgSRNWAgAAAOTcBLlOZ26w149sTupTT75TScm2Dq2YwXMCikq3z16Mv27soN/PkyQAAADyb4Jcp/oeyVFSMS+N5TvxWrWsUNCjvLmu1NUlBYMpT351YSnYM7JfiRYhAAAAmEnBoOTxSOOKeuP1avfGg/b6zuWJBT/5TmWJPfQoX6FQfN+RCQQS9iQNP9SRsF+JPUkAAACYUX6/1NGRkOHktLereslSVS9ZmpL5RL5TeWIPfQbsoS9R7EkCAABAMZggw2nCzCeUBPbQA5NhTxIAAACKwSQZTmkzn1BWKOhRnkZ6zTvsSQIAAECRyjrzaZLcKBQ39tCjPKXrNT9uT5KTtF+JPUkAAACYTSbrUT/+Qr/60sYe+gzYQ1+6Mu47ouc8AAAAZqNJ8qC6fWPD6sJkQxUr9tADWZh03xE95wEAADAbTZIHNb6gD/aQDVXqKOgBAAAAoJhM0qN+/ESV43aTDVXi2EOP8uG6Umen/f+IurDU8PJIkAgAAABQDCbpUV9TWRO/0K++9LGHPgP20JeIUEimpUVOLCbj8SjatkUDwwOq+cxt8hrZxPuODqm5udBnCgAAAGQni8ynSDSihtZarTwqbfryHlWtvJTU+yKQbR1KQZ8BBX0JmCA0xDGSd/w4AkIAAABQYgba21SxrjU+iTV0/SdVsesf7Wtjj8fO9DOpNetkW4ey5B6lb4LQEG/yuNGAEAAAAKAUuK4q198SD8ZzYjFV7Nw19to4FpPWrk3YkoriQkGP0hcMyngSf9SNxyPjOInjCAgBAABAKUkzseUkj2FSq6hR0KP0+f0pYSBOR4ecBx9MCBIhIAQAAAAlZTQNf5yU/dZMahU1CnqUhaGbmnTmBqmhSep/8aDdJ9TcbPfMd3ba/7N3CAAAAKUkTRr+0OrrSb0vIfShR/GbQkpnyhIjv58nMAAAAJSu5mapsTGehh9duEDLTt2l+h5p98aDql6ytNBniGmgoEdxS9OObuimppRhww916Mhm2XTPnctJ8wQAAED5GD+JFY2o2yd1+yTjryvseWHaKOhRvFw3XsxLNrXTu65VZx9qVbdvbFhdWPFifnSc1q6171QyOw8AAACgSLGHHsVrgnZ09T2Jw4I9Y8V8HGmeAAAAAIocM/QoXiPt6MYX9cbr1e6NBxOWDzlut8zO5YnFP2meAAAAKFN1YTvp5dm7T4oOZ5VFhdmJGXoUr3Tt6NrbVb1kqWoqa+KX6iVL5SSle5LmCQAAgHJUsW2HjmyWOndI8957mbRqlRQISKFQoU8NJ8ExxqS0IsSY3t5e+Xw+hcNhzZ8/v9CngySRaETL7qwdSek8NHlKp+vG0z0p5gEAAFB2XFcmEEjZtirJTnodPszr5Fki2zqUJfcoelmndNKiDgAAAOUsTQZV3GjGFK+XiwpL7gEAAACgHASDkmeCEpCMqaJEQY/i4rpSZ6f9/4i6sNTwsg2/AwAAADABv18aly01uvfakDFVtFhyj+IRCsX7zhuPR9G2LRoeHoj3mDc7l9snqObmQp8pAAAAMDs1N0uNjep/4Ze69NEPqmZQ2r3x4ORZVJi1CMXLgFC8WSJNgMeQIzlG8o4fR5gHAAAAkFEkGlHtplpJUt9dfaqprCnwGWG8bOtQltyjOKQJ8KhILualsTAPAAAAAChxFPQoDsGgTFKAh/F4ZBwncRxhHgAAAADKBAU9ioPfr2jbFg2N1O/G65XT0SHnwQfjoR4izAMAAABAGSEUD0Vj6KYmnX2oVfU9ScEdjY12mX19PcU8AAAAkKW6sBTsGekWNT4Uz3Wlri7b5o7X17MaM/QoKt0+ac9ZkvHXjR30+6WGBp5sAAAAgCxVbNuhI5ulzh1SVXC5BtrbFIlGNNDeJhMISKtWSYGAFAoV+lQxCQp6AAAAACgnrqvK9bfIO9LvzInF5F3XqobWWlWsax0Lo47FpLVr7Yw9ZiUKegAAAAAoJxN0kFp5VPEiP44uUrMaBT0AAAAAlJNgUEruIOX1atOX96R0lqKL1OxGQQ8AAAAA5cTvlzo6ErpFOe3tqlp5aUpnKbpIzW6k3KOoXOBK731F8uzdJ628tNCnAwAAABSn5ua03aIm7CyFWYmCHkWj8ua1em6n5EgyT14mNTVJ27cX+rQAAACA4uT3p5197/bZS0JnKcxKLLlHcdi7VxU7d2lk9Y/9/44d0t69BTwpAAAAACgcCnoUh5/8JF7MJ/jpT2f6TAAAAICSVheWGl6WHLd74kGuK3V20tKuwCjoURwuuUTJHTQkSStXzvSZAAAAACWrYtsOHdksde6QqoLLNdDepkg0knAZaG+TCQSkVaukQEAKhQp92mXLMcakrZNg9fb2yufzKRwOa/78+YU+nbI2+Kkb4svujSSHPfQAAABA7riuTCCQ0KN+yJHO3GD31Et29v7I5qR+9V6vdPgwafg5lG0dygw9ikb0oXa9+2ZpQ6N04uk9FPMAAABALnV1JRTzklRhpPqesY+DPUnFvCQND9u0fMw4Uu5RVJ7328tXVpxf6FMBAAAASkswKHk80rii3ni92r3xYDzx3nG7ZXYuTyz8vV7b+g4zjhl6zE4ThGxkFdABAAAAYOr8fqmjwxbokuT1ymlvV/WSpaqprFFNZY2qlyxVtG2LhkYSq43XK7W3s9y+QNhDnwF76AsgFJJpaZETi8l4PPYJ46YmDT/UoZrP3CavkYzHI6ejQ2puLvTZAgAAAKXFde0S+vr6tIV6JBrRsjtrVd8j7d54SNVLlhbgJEtbtnUoS+4xu7huvJiXJCcWk3ddq977fKueDY3t13FiMWntWqmxkXcDAQAAgFzy+yd9je243broqNK3lcaMYsk9ZpcJgjhWHiV8AwAAACi4UEhV9efo249Jjz4mVdWfQ9u6AqKgx+wSDMp4En8sjderTV/ek3Kc8A0AAABgBrmuzJo1csbt2naMsStnk7KvMDMo6DG7+P0pIRtOe7uqVl5q98yPC+ggfAMAAACYQV1dCcV8HCtnC4ZQvAwIxZt5k4ZsZAjoAAAAAJAnritzxhmpRb3XKx0+zOvzHMq2DmWGHrNSt0/ac5bi/S7j/H6poYEnCwAAAGCm+f2KfmOrhscf83hYOVtApNwDAAAAALIydFOTzj7UqouOSjs/+rDmXXo5xXwBMUMPAAAAAMhat0967Dxp+JqPUcwXGAU9Cs91pc7OhGTMurDU8LLtcQkAAAAASMWSexRWKCTT0iInFpPxeBRt26Lh4QEd2Wz7zpudy6WODqm5udBnCgAAAACzCgU9Csd148W8JDmxmLzrWlVjpJHmdPZza9dKjY0s5wEAAACAcVhyj8Lp6ooX86MqxhXzcfS1BAAAAIAUFPQonGBQxpP4I2g8HhnHSRzn9dq+8wAAAACAOAp6FI7fr2jbFg2N1O/G65XT0SHnwQdtES/Z/9PXEgAAAJg1phRgnSYAG7nDHnoU1Ggfy/oeaffGg6pestR+orHRLrOvr6eYBwAAAGaJim07EgKsB9q2aOimpgnHVq6/xW6z9XgIu84DCnrkl+tKXV1SMDhpYe4kH/D7KeQBAACA2cR1bYFu7IejodZnH2pVty9xaF1YOrJZ8bEi7DovWHKP/AmFZAIBadUqmUBAA+1tikQjCZfhhzp0ZLPUuUOqCi6XQqFCnzUAAACAdCYIta7vSR0a7LGz+AkIu845xxiT/DBjnN7eXvl8PoXDYc2fP7/Qp1M8XFcmEEj4hR9ypDM3KP7u3ei7dgm/6F6vdPgw79oBAAAAs43rSoGAnW0fYbxe9b94UMZflzDUcbtVFVye+AYAr/Wzlm0dygw98iOLd+941w4AAAAoIn6/3Qc/LsDaaW9X9ZKlqqmsSbhUL1maEoBN2HXuMUOfATP0JynNDH3yu3e8awcAAAAUIdfNKsA6Eo2oobVWV74offF/PKCqj13D6/wsMUOPwkrXki7p3bvqJUvlJL3Dx7t2AAAAwCzn90sNDRlft1ds26GfPyTd/WOp6rOfk844g8ysHGOGPgNm6E9eJBrRsjtrR1rSHRprSZcsy3f4AAAAABSJNCt2Jdn2dUeO8Lo/g2zrUNrWIa+6ffaSHJKRgBZ1AAAAQGlJk6klyQbqvfQSr/9zhCX3AAAAAIDcCgbtbHwyj8euzEVOUNADAAAAAHJrJBHfjCvqjePYlHxm53OGgh4AAAAAkHvNzervekHXXiNde43U/9KvpebmQp9VSWEPPQAAAAAgL4y/To+dZ69vnyxXCyeFGXrkVV1YuuaA5P32d2yaPQAAAAAgJ5ihR95UbNuhVx4YedfosSbJcaQHH2SZDQAAAADkADP0yA/XVeW6zyT+gBkjrV3LTD0AAAAA5AAFPfKjq0uOManHh4dt30kAAAAAZaEuLDW8LDlu99hB15U6O5nsmyaW3CM/gkG7xD65qPd66TsJAAAAlImKbTt0ZLPkNZLZuVwDbVskSZXrb5ETi9m+9B0dbMs9SY4x6aZRMaq3t1c+n0/hcFjz588v9OkUl1BIZs2a+Ey98Xjk8MsKAAAAlAfXlQkEbOE+YsiRHCN5x4/zeqXDh+lPP062dShL7pE/zc3qf+nXY30nu16gmAcAAADKRVdXQjEvSRXJxbzEttxpYMk98oq+kwAAAECZCgbtkvpxRb3xeCRjEvO22JZ70pihBwAAAADknt9v98d7R+bkvV45HR2KfmOrhhx7yHi9Uns7y+1PEjP0yB3Xlbq67Dtx434h68JSsGck1XLJ0gKeIAAAAIAZ1dwsNTbaJfX19ZLfr6FoRGcfalV9j7R740FVUyOcNAp65EYoJNPSouOxeapwhqVv3K+hm5o09GCHDj5QLa+kqp3L4wmWAwPS0JA0Z45UWWlvwhjp+HF7vbrahuRLUjQqDQ5KFRXS3LljdxmJTH1sVZVd9SPZcdGofcNw3ryTG3v8uD3vefPG3ngcGpIGBuzXVlWd3Nj+frsyae5c+2+R7NaiEyemNtZx7OMz6sQJ+7nKSvvYT3VsLGbvT5JqasbGpvt+TmVspu99Ln5Oxn8/c/Fzku77mYufk9Hv53R/TpK/n9P9OZno+zndn5Px38/p/pzwHMFzRDZjeY7gOWIUzxGZx/IcwXPEyYxN+71f7Ff/AjvhN/rt7PbZi2Fb7vQYTCocDhtJJhwOF/pUZq+jR03M4zFGMpIxf6MvmUFH5oKbZV7TqcY+BRn7H6/XmKNHzWc/az/80pfGbqavz8TH9vWNHf/Sl+yxz3428W5Hx77xxtixv/kbe+zmmxPHVlfb4y+/PHbsgQfsseuuSxx76qn2+IEDY8c6OuyxD384cWwgYI8/99zYsW9+0x57//sTx557rj3e2Tl27PHH7bGLL04ce8EF9vh3vzt27Mkn7bF3vCNx7GWX2eOPPjp27Omn7bH6+sSxH/ygPb5t29ixX/zCHlu8OHHsNdfY41u3jh178UV7zOdLHNvUZI/fd9/YMde1xyoqEseuX2+P/+Vfjh07dmzs+xmNjh2/4w577I47xo5Fo2Njjx0bO/6Xf2mPrV+feH8VFfa4644du+8+e6ypKXGsz2ePv/ji2LGtW+2xa65JHLt4sT3+i1+MHdu2zR774AcTx9bX2+NPPz127NFH7bHLLksc+4532ONPPjl27LvftccuuCBx7MUX2+OPPz52rLPTHjv33MSx73+/Pf7Nb44de+45eywQSBz74Q/b4x0dY8cOHLDHTj01cex119njDzwwduzll+2x6urEsTffbI//zd+MHXvjjbHv53g8R1g8R1g8R4zhOcLiOcLiOcLiOWJMsTxH9A30Gd0to7tl+gb6DFJlW4cyQ4/p6+rS8dg81cq+LRlRjSqMtPLoZAmW7JEBAAAAytXotlzP3n1SdDhl2y6yQx/6DOhDnwXXVd8Zy3WKeVOS1KMF+j3vmzqx54eae8nl6jd2zVCNjsd7TA681c9SuUnGslTOXmepXHZjWU7Lc4TEcwTPETxH8BwxNpbnCHud54jsxs70c4TXK9146Yvy7N2r/6VmzdWAHMme4Mj2XGRfh1LQZ0BBn50T/9CmY+v+UhWSft9zTJ6OdvvLGApJa9fa3+rRBEt+SQEAAICyFHmxW7XL7L75PtXYSb9RI5N/zNRnX4ey5B45MfzpJq14cTSp8tBYUmWaVEsAAAAA5anySJce0FftdUUTPzm6PZeaIWsU9MiZCZMq/X5+KQEAAABozvJ6bfBssevwk3m9dhIQWfMU+gRQGqJRST/+kvTjL9nrAAAAAJDM77d75Uc2+Y/u/zaj23OZCJwSZugxNa4rdXWlpFAODkr64VckSUOHu6TzggU6QQAAAACzVSwmvfK+ZuknH9Rbe/er4bEPqmZQ2r3x4Ni2XWSNgh7ZC4VkWlrkxGIyHo+ibVs0dFOTJMl5OKRmVcmRdMof3io9uJXwOwAAAAAJ+vuls86SpD/Qb3rm6/ln7fGUbbvICgU9suO68WJekpxYTN51rTr7UKsk6chm6aHRsUY22b6xkSUzAAAAABKMb3OH6aGgR3a6uuLF/KgKI9X3SI4kb3LzQxIqAQAAACSpqZEiEXs9QvbWtFHQIzvBoIzHk1DUG69XuzcetNd3Lk8s+EmoBAAAAIC8IuUe2fH77Z55x35ovF457e2qXrJU1UuW6viW/6Ua9alGfYp4TiGhEgAAAEBGdWGp4WXJs3ef1NlpQ7iRNccYk7xYGuP09vbK5/MpHA5r/vz5hT6dgopEI1p2Z63qe6TdGw8lpFBGIlJtrb3ed6hbNUsJtQAAAACQaGBA+sxn7PW/e8c/qObWdfIaG8PlSJLHY9valXnAdrZ1KAV9BhT0YyLRiGo32aq9764+1VTWxD8Xi0mvvGKvn3GG/T0EAAAAgPHGTwS+6ZyiWtOXOsjrlQ4fLusVv9nWoeyhR054PNKZZxb6LAAAAADMZnPmSH/zN5L+679U+b8G0g8iYDtrFPQAAAAAgBlRWSn9+Z9Lciul7cNSLM0gArazxsJoZMd15fnRHl3g2tAKx+1O+PTgoLR5s70MDhbkDAEAAAAUC7/f7pX3eiXZPfSSDd8mYDt77KHPgD30kkIhmZYWObFYPKzCeDxyxoVVJITi9dn+kgAAAAAwnjHS//2/9vqpp0pOt6v+F36pSx/9oGoGU8O3yxV76JEbrhsv5qWR5EnJfrx2rdTYKPn98nql666znxt5kw0AAAAAEhw/Li1caK/39Uk1fr9iCxfo+WfsMeOnW9ZUUNBjcl1d8WI+xbiwinnzpF27ZvbUAAAAAKCcUdBjcsGgXV6frqgnrAIAAADAFNTU2GX3yA1C8TA5v1/Rti0aGllrH//dI6wCAAAAQI7UhdOHb8t1pc5O+3+koKBHRkM3NenMDVJDk3Ti6T32F+rw4XggnmRD8d76VnuJRAp2qgAAAACKTMW2HTqyWercIVUFl2ugvU2RaEQD7W0ygYC0apUUCEihUKFPddYh5T4DUu6lSDSi2k02wr7vrj7VVKZG2JNyDwAAACCTgQHpi1+01++9V5r7W1cmEEjY4jvkSBc1S8+GJO/4atXrtROLZbBKmJR7zKiqKunAgbHrAAAAAJBsaEj6+7+317/yFWlumhDuCiOtPJpUzEsJodywKOiREx6P9La3FfosAAAAAMxmc+ZIX/rS2HUFg7aYGFfUG69Xm778Q5mnLk8s9gnlTsEeegAAAADAjKistDPzX/mKvS6/X+rosMW6JHm9ctrbVbXy0sRwbkK502KGHhk5breuPWAT7h23W1qyNGXM4KC0fbu9fuONI++2AQAAAEAmzc1SY6NdTl9fHy/ah25q0tmHWlXfI+3eeFDVaeqQckcoXgZlH4oXCsmsWSNn5MfEOI6cBx9MSLiXCMUDAAAAkJkx0vHj9np1teQ4E4/NJpy7VBGKh+lzXZmWlngxL8leb2mx76CNW+7i9Uof/vDYdQAAAABIdvw4E4G5REGPiaVJnJRkAyuS0iXnzZP++Z9n7tQAAAAAoNwRioeJBYMynjQ/Ih4P6ZIAAAAApqy62s7M9/XZ65nUhaVrD0ieb39Hct38n2CRoaDHxPx+Rdu2aHj8vhbHsSmUpEsCAAAAmCLHscvsa2om3z8vSRXbduiVB6RHH5OqbmiSzjhDCoVm5kSLBKF4GZR7KF4kGtGyO2t10VHp4Y8+rKpLL09bzB8/Lp17rr1+8GB277YBAAAAQFquKxMIpG4B9nikI0dKfoIx2zqUGXpk1O2THjtPil3zsQl/cYyxv1dHjtjrAAAAAJAsGpX+/M/tJRqdZGCmPC9IIhQPOTJvnvTcc2PXAQAAACDZ4KB0zz32+pe+JFVWTjAwGLSz8elm6MnziqOgR054vdKKFYU+CwAAAACzWUWF9NnPjl2fkN8vdXTYNtojRb1xHDnkeSWgoEcq15W6uuy7YgsXqC4sBXskx+2Wliwt9NkBAAAAKFJz50qbN2c5uLlZ/ZdfoqYvLpMk7bj316qmHklAQY9EoVD8XTDj8cjzyWt05FuS10hm53KbcN/cnPJlQ0PSP/2Tvf6JT2R4tw0AAAAAsmD8dXrsPHt9u7+usCczC5Fyn0FZpdynSZI0khK6SXi90uHDKctcIhGpttZe7+uzbSgAAAAAYDoi0YhqN9lCo++uPtVUlkehkW0dyjwqxqRJkkxpDTk8bFMlkwp6j0d6//vHrgMAAABAMiYCc4uCHmOCQRmPJ/MMfZpUyaoq6amn8n6GAAAAAMrMaKaXZ+8+KTpss74IxpNEH3qM5/cr2rZFQyMVvPF65TQ12SJesv9vb+eXBwAAAMBJqa6W3njDXqqrM4+v2LZDRzZLnTukee+9TFq1SgoEpFAo7+daDNhDn0FZ7aGX3aOy7M5a1fdIuzcesimSrmuX2dfXU8wDAAAAmBlpMr7iJsj2KhXsocdJ6/bZixlNkfT7M/6iHD8+1od+797s3m0DAAAAgAmlyfiKmyDbq9xQ0CMnjJEOHhy7DgAAAADJolHpq1+11z//eamycpLBwaBN3J5ohj5Ntle5YQ89cmLePKmz017mzSv02QAAAACYjQYHpb/4C3sZHMww2O+XOjrimV6j84aGbK84ZuiRE16v1NBQ6LMAAAAAMJtVVEg33zx2PaPmZqmxUf0v/FKXPvpB1QxKuzcetFlfoKBHqgtc6b2vjLSFWHlpoU8HAAAAQImYO1d68MEpfpHfr9jCBXr+GfthPOsLFPRIVHnzWj230/aeN09eJjU1Sdu3Z/y6oSHpu9+116+6Kst32wAAAAAAJ4099Bizd68qdu7SSBt6+/8dO2xsfQYDA9JHP2ovAwP5PEkAAAAAgERBj/F+8pN4MZ/gpz/N+KUej3Txxfbi4acKAAAAQBqRiFRTYy+RSKHPpvixMBpjLrlERkot6leuzPilVVVZ1f0AAAAAytzx4yf3dXVhKdgjOW63lC4Uz3Wlri7b7q5MEvCZS8WYFSs0tPr6sXYQkt1Dv2JFAU8KAAAAQKmoqpJeftleqqqy/7qKbTt0ZLPUuUOqCi7XQHubItFI/DLQ3iYTCEirVkmBgBQK5e3fMJs4xhiTeVj56u3tlc/nUzgc1vz58wt9OnkXiUbU0FqrlUelTV/eoypS7gEAAAAUkuvKBAJyYrH4oSFHOnOD1O2zM/dHNkve8ZWt1ysdPly0M/XZ1qHM0CPF837p7y+SYivOz/pr+vvtRP6KFfY6AAAAAOREV1dCMS9JFUaq77HXgz1JxbwkDQ9LL700M+dXQOyhR07EYtLzz49dBwAAAIBkg4PS179ur7e2SnPmZPFFwaBN3h5XaBivV7s3HpTx18lxu2V2Lk8s+r1eqb4+tyc/CzFDX65cV+rstP9PUheWGl4eCZvI0ty5tg/9d79rrwMAAABAsmhU+tzn7CUazfKL/H6po8MW6ZLk9cppb1f1kqWqqaxR9ZKlirZt0dBIurfxeqX29qJdbj8V7KHPoCT30IdCMi0tcmIxGY/H/vDf1CRJGn6oQzWfuU1eIxmPR05Hh9TcXOATBgAAAFAKTpwYKy9CIWnevCl8sevaZfT19SnFeiQa0bI7a1XfI+3eeEjV6VLwi0i2dSgFfQYlV9BPEighlV6YBAAAAIDSF4lGVLupVpLUd1efaiprCnxG05NtHcoe+nIzSaCEo0nCJDIU9MPD0g9/aK+vWjW2GgYAAAAAkB952UPf3d2tG264Qb//+7+v6upqvfOd79S+ffvinzfG6O6779bixYtVVVWlhoYG/epXv0q4jYGBAd1yyy069dRTVVNTo6uvvlpu0n7vY8eOafXq1fL5fPL5fFq9erV+97vfJYx55ZVX9KEPfUg1NTU69dRTdeuttyqa9WaNEhQMyngSv+02UOKQvrfxUMrnsg2TOHFCuuIKezlxIpcnDAAAAABpJOWCnUwWWLHLeUF/7NgxrVy5UnPmzNH3v/99HTx4UH/3d3+n3/u934uPue+++3T//fdr69at2rt3rxYtWqQPfOADevPNN+NjNmzYoMcff1yPPPKInn76afX19emqq67S8PBwfMx1112n/fv364knntATTzyh/fv3a/Xq1fHPDw8P68orr1QkEtHTTz+tRx55RN/5znd0++235/qfXTz8/pTAiNFAieolS+2e+XFhE9mGSXg80jveYS/J7wkAAAAAgCRFItJb32ovkcg0bigUkgkEpFWrZAIBeT79aR3ZLHXukKqCy+0G/TKQ8z30d955p37605/qJz/5SdrPG2O0ePFibdiwQV/84hcl2dn40047Tffee6/Wrl2rcDist771rdq5c6c+8YlPSJJeffVVnX766dq9e7caGxv1wgsv6Nxzz9Wzzz6rCy+8UJL07LPP6qKLLtKvf/1rLVu2TN///vd11VVX6ejRo1q8eLEk6ZFHHtGNN96oN954I6s98SW3h15ZBEZMEjYBAAAAACcrEpFq7VZ39fVJNSez1T1NLpiR3UIcV+RZYNnWoTmfS/2Xf/kXXXDBBbr22mu1cOFCvetd79KDDz4Y//zLL7+s119/XVdccUX82Ny5c3XZZZfpmWeekSTt27dPg4ODCWMWL16s8847Lz7mZz/7mXw+X7yYl6T3vOc98vl8CWPOO++8eDEvSY2NjRoYGEjYAjDewMCAent7Ey6lqNsn7TlLMv661E/6/VJDQ9H+8AMAAACYnaqqpAMH7KWq6iRvJE0umJM8ZjQLrMTlvKD/r//6L33jG99QMBjUv/3bv+nP/uzPdOutt+rhhx+WJL3++uuSpNNOOy3h60477bT4515//XVVVlZqwYIFk45ZuHBhyv0vXLgwYUzy/SxYsECVlZXxMck2bdoU35Pv8/l0+umnT/UhAAAAAACk4fFIb3ubvZz0Vt10uWDJY7LMAit2OS/oY7GY/uiP/kj33HOP3vWud2nt2rVas2aNvvGNbySMc5zE91CMMSnHkiWPSTf+ZMaMd9dddykcDscvR48enfScYPX320n9hgZ7HQAAAADyIl0uWFPTSWWBFbucF/R/8Ad/oHPPPTfh2PLly/XKK69IkhYtWiRJKTPkb7zxRnw2fdGiRYpGozp27NikY37zm9+k3P9vf/vbhDHJ93Ps2DENDg6mzNyPmjt3rubPn59wQWaxmLRnj70krX4BAAAAAEnS4KD04IP2Mjh48rczdFOTztwgNTRJ/S8elLZvt3vmOzvt/5ubc3PCs1zOC/qVK1fq0KFDCcdefPFFBQIBSdJZZ52lRYsW6amnnop/PhqNas+ePbr44oslSeeff77mzJmTMOa1117TgQMH4mMuuugihcNhPffcc/ExP//5zxUOhxPGHDhwQK+99lp8zJNPPqm5c+fq/PPPz/G/vLhc4EobnpE8e9NnCUzV3LnSo4/ay9y5OblJAAAAACUmGpVaWuxlut3EU3LByjALrCLXN/i5z31OF198se655x59/OMf13PPPaeOjg51dHRIskvgN2zYoHvuuUfBYFDBYFD33HOPqqurdd1110mSfD6fmpubdfvtt+v3f//39Za3vEV33HGH3v72t+v973+/JDvr/8d//Mdas2aN2tvbJUktLS266qqrtGzZMknSFVdcoXPPPVerV6/WV7/6VfX09OiOO+7QmjVrynrmvfLmtXpupw2OME9eJjU12Xe0pqGiQrr22pycHgAAAIAS5fVKH/7w2HVMT87b1knSd7/7Xd11113q6urSWWedpdtuu01r1qyJf94Yo7/6q79Se3u7jh07pgsvvFBf//rXdd5558XHnDhxQp///Of1rW99S/39/Xrf+96ntra2hJC6np4e3XrrrfqXf/kXSdLVV1+trVu3JvS8f+WVV7R+/Xr98Ic/VFVVla677jp97Wtf09wsp5FLrm3d3r0y7353agrkc89JK1YU4owAAAAAYEoi0YhqN9n+d3139amm8mT6381e2daheSnoS0nJFfT33y/dfnvq8QcekDZsOOmbHR6Wnn3WXn/Pe3i3DQAAAED+UNBbOV9yj1nukktklKZP48qV07rZEyek977XXu/rk2pK6/cJAAAAwCxTF5aCPSO5YNFhKRgsq/3zUh5C8TDLrVihodXXx/s0GsnuoZ/mcnvHsW0e6+vtdQAAAABIdvy4dOaZ9nL8+MnfTsW2HTqyWercIc1772XSqlVSICCFQjk60+LAkvsMSm7JvezylIbWWq08Km368h5Vrby00KcEAAAAoAxEIlKtXSl/8it7XVcmEJCTrl+212vb1hX5TD1L7jGp5/328pUV5d2+DwAAAMDMmTfP5nGPXj8pXV3pi3nJhnu99FLRF/TZoqAHAAAAAMwIrzcHzbWCQcnjkSaaoa+vn+YdFA/20CMnTpyQrrzSXk6cKPTZAAAAAChZfr/U0RFvrRXPB/N6pfb2spmdl5ihR44MD0u7d49dBwAAAIBkQ0PSP/2Tvf6JT0gVJ1uRNjdLjY3qf+GXuvTRD6pmUNq98aCqlyzN2bkWAwr6MpXrFg+VldK2bWPXAQAAACDZwIB0ww32+kc+Mo2CXpL8fsUWLtDzz9gPjb9uuqdXdCjoy9BoiwevkcyOy+xBj8cuW2luPqnbnDNHuvHGnJ0iAAAAgBLk8Ujvf//YdUwPBX25cV1Vrr9FzshGk3jL+FhMWrtWamwsqz0nAAAAAGZOVZX01FOFPovSwXsi5SabFg8nYXhY2r/fXthDDwAAAAD5xwx9uclTi4cTJ6R3vcte7+uTamqmcY4AAAAAkKXRfDDH7ZYqq6WurmlnhBULZujLTZ5aPDiOtHixvThO5vEAAAAAys/x49Lb3mYvx49P//ZG88E6d0hV9efInHGGtGqVFAhIodD072CWc4wxJvOw8tXb2yufz6dwOKz58+cX+nRyx3WTWjwcKrsWDwAAAABmViQi1dba69Ne2eu6MoHAxFuKvV7p8OGinKnPtg5lyX25osUDAAAAgBk2b57U2Tl2fVomyweTxjLCirCgzxYFPQAAAABgRni9UkNDjm5ssnyw0Ts7yYywYsEe+nLguvZtMNdN+VRdWGp4eSRAYhpOnJCuvdZeTpyY1k0BAAAAQGbJ+WAej0Ybbk03I6xYsIc+g6LfQx8KybS0yInFZDweRdu2aOimJknS8EMdqvnMbfIa+8PvdHRIzc0ndTc53QsDAAAAoCQNDUnf/a69ftVVUkUu1oy7rvTSSzp+xmIt3bpM9T3FnxGWbR1KQZ9BURf0aUIihhzpzA32+pHNknf8d38aoRGDg/bNMUlqaZHmzDnZkwYAAABQqvI5ERiJRlS7yd543119qqks3llGQvGQNiSiwkj1PZKjpGJemlZoxJw5UmvryZ8qAAAAgNLn8UgXXzx2HdNDQV/KgkG7lH5cUW+8Xu3eeNBe37k8seAvg9AIAAAAAIVTVSX99KeFPovSwXsipczvt3vmHfuh8XrltLereslSVS9ZavfMjwRIaJqhEbGY1NVlL5N1jgAAAACAfJkw9HuSoPBixh76DIp6D73sPpJld9ZOHAwxEiCh+vppJUASigcAAACgkAba21SxrjUe+j0aCF6xbYcq199iVyd7PDb86yTDwGcKoXg5UgoF/UwEQ0QiUl2dvd7dTUEPAAAAIFV/v3Tppfb6j39sl+DnxASB4Bc1S8+GchcGPlMIxcOMqqmRfve7Qp8FAAAAgNksFpOef37ses5MEAi+8mhuw8BnGwp6AAAAAMCMmDt3rA/93Lk5vOFg0C6nTwoE3/TlH8o8dXnJhoETileKkgIfJgyGAAAAAIAZVFEhXXmlvVTkcnrZ77d748eFfjvt7apaeWlKUPh0wsBnG/bQZ1B0e+hDIZmWFjmxmIzHoxOfvEaV33o0Hgzh5CkAYmBAWrvWXm9vz/G7bQAAAACQjTSh3xmDwmchQvFypKgK+jRBEEaSM35MngIgSLkHAAAAkMnwsPTDH9rrq1aNTajn00wFhecSoXjlKE0QhJM8Jk8BEHPmSPfdN3YdAAAAAJKdOCFdcYW9zkTg9FHQl5Jg0C6rzzRDn4cAiMpK6fOfz/nNAgAAACghHo/0jneMXcf08BCWEr8/JfDBaWpKCIYopQAIAAAAAMWlqkrav99ectaDPgsXuNKGZyTP3n0zd6czgD30GRTVHnpNEPiQJhgi12Ix6bXX7PU/+APebQMAAAAwOwx+6gZV7NwlRyMrmJuapO3bC3xWk8u2DqXsKkHdPmnPWZLx19kDfr/U0JDXmfn+fnvzfr+9DgAAAAAFt3dvvJiXRrYj79gh7d1bwJPKHQp65ExFRY57SQIAAAAoKf39dq6xoWGGJgJ/8pPUoHBJ+ulPZ+DO84/yCzlRUyMNDhb6LAAAAADMZrGYtGfP2PW8u+SS1KBwSVq5cgbuPP+YoQcAAAAAzIi5c6VHH7WXuXNn4A5XrNDQ6us1GhxnJKmpSVqxYgbuPP+YoS8xjtutaw+MhD243dKSpYU+JQAAAACQZLfoXnvtzN5n9KF2XTx3l1YelTZ9eY+qVl46syeQR8zQl5JQSFX15+jRx6RvPyZV1Z8jhUIzctcDA1Jrq70MDMzIXQIAAABAVp73S39/kRRbcX6hTyWnKOhLhevKtLTIGdeF0DFGammxbevybGhIamuzl6GhvN8dAAAAgCI0PGzz6H76U3sd08OS+1LR1SUnXapELGZ70OexZZ0kzZkj/eVfjl0HAAAAgGQnTkjvfa+93tdnw7Vx8ijoS0UwKOPxpBb1Ho9UX5/3u6+slO6+O+93AwAAAKCIOc5YeeKk7SeXQ65rJz4DdaoLS8Ge0ssZY8l9qfD7FW3bouHxvxSOI3V05H12HgAAAACyUV0tdXXZS3V1Hu8oFJIJBKRVq1RVf45eeUDq3CFVBZfPWM7YTHCMGbfpGil6e3vl8/kUDoc1f/78Qp/OpCLRiJbdWauLjkoPf/RhVV16+YwV88ZI4bC97vPNwLttAAAAAJCO68oEAum3JEuS1ysdPjyrJz6zrUOZoS8x3T7psfOk2DUfm9Ef0OPHpQUL7OX48Rm7WwAAAABINFG+2KjhYZszVgIo6AEAAAAAM+LECenKK+3lxIk83clIvtiEvN4ZyRmbCRT0yInqaikatZe87oUBAAAAULSGh6Xdu+0lb23rRvLFhka2ARvHsWHhki3m29tn9XL7qSDlHjnhOLSrAwAAADC5ykpp27ax6/kydFOTzj7UqvoeaffGX6u6stous6+vL5liXqKgLx2uK8/B/9QFrlQ7WHrtGAAAAAAUvzlzpBtvnJn76vbZi/HXSZU1JVXIj2LJfSkYaclQ1XilnnuoMO0YolHp85+3l2h0xu4WAAAAAMoWBX2xc12ZlpZ4iuNotzgnFpPWrpVcd0ZOY3BQ+trX7GVwcEbuEgAAAECRGR6W9u+3l7ztoS8jLLkvdpO1ZBhtxzADS0vmzJHuuGPsOgAAAAAkO3FCete77PW+PqmmprDnU+wo6IvdSEuGtEX9DLZjqKyUvvrVGbkrAAAAAEXKcaTFi8eu51NdWAr2JOWLua7U1SUFgyWxp54l98UuuSXD6PESa8cAAAAAoPhVV0vd3faSz3bXFdt26MjmsXyxgfY2DbS3yQQC0qpVUiAwo5lj+eIYY0zmYeWrt7dXPp9P4XBY8+fPL/TppBWJRrTszlrV90jfX7NHVYOxGW/HYIw0NGSvV1Tk/902AAAAAEjLdWUCgYRVzEOO5BjJO36c1ysdPjwrJ0GzrUNZcl8iRlsyxFacb1syzLDjx6XaWnudvTAAAAAACiZNzlhFumnsGcwcyxeW3AMAAAAAZsSJE9K119rLiRN5upNgUPIklrrG45FJXkY8g5lj+UJBj5yorpaOHbOXfO6FAQAAAFC8hoelxx6zl7y1rfP7pY4OW7BLktcrp6ND0W9sHcseK5HMMZbcIyccR/q93yv0WQAAAACYzSorpa1bx67nTXOz1Nhol9SP5IsNRSM6+1Cr6nuk3RsPqno0+b6IUdCXiLQtGUaVWGsGAAAAAMVpzhyptXWG7szvT6l/RrPHjL9uhk4iv1hyXwLStWSIRCOKRCMz1pohGpXuvtteotG83AUAAAAAYBza1mUw69vWTdCS4cwN9vqRzZJ3/Hc4T60ZIhFS7gEAAABMLhaT/s//sdfPPjsluy6vItGIajfZoqXvrj7VFKA7WLZoW1cuJmjJUN8jOUoq5qW8tWaoqJDWrx+7DgAAAADJ+vulpSM7hJkInD5Kr2I32pJhXFFvvF7t3njQXt+5PLHgz1Nrhrlzpa9/Pec3CwAAAKDE+HwFuFPXlefgf+oCV6odnCB7rAixh77YpWvJ0N6u6iVLVb1kqaJtW0quNQMAAACA4lRTI/3ud/YyY7PzoZBMIKCqxiv13ENj2WP5yhebSeyhz2DW76Ef5boJLRlGRaIRLbuzdqQ1w6GSaM0AAAAAAFlJkzkWl6d8sVxgD325SdOSYdRMtGaIRMb60M/ou20AAAAAMJE0mWNxecoXm0ksuUfODA3ZCwAAAACkMzAg3XijvQwMzMAdBoMyE0Xp5ylfbCZR0CMnqqrsqn/XtdcBAAAAINnQkLRjh73MyGSg35+YKzZ6vETyxVhyX+Ict1vXHrA/uPlMcvR4pLr8regHAAAAUALmzJHuu2/s+kwYuqlJZx9qVX2P9P01e1Q1GEvJHitWFPSlLBRS1Zo1enTkbSjznXOkBx+UmpsLe14AAAAAylJlpfT5z8/8/Y7misVWnC9Vlk7gF0vuS5XryrS0yBnXxMAxRmppsevicywalb76VXuJRnN+8wAAAACAJBT0pWqiNMdYzCY55tjgoPSFL9jL4GDObx4AAABACYjFpO5ue5kofB7ZY8l9qRpJc0wp6j2evCQ5VlRITU1j1wEAAAAgWX//2Nb1vr48tbveu1f6yU+kSy6RVqyQJNWFpWBPfnPFCoHSq1SNpDlW/FmrvKPHHEfq6MhL+MPcudL27Tm/2dnNdaWuLikYLIlAjVmHxzd/eGzzh8c2v3h884fHNr94fPOHxzZ/8vjYVlQYyRip+zVpaW6TtU1Tk/Tww3Jkg8GHVl+v4fecryObJa+RzM7ltiYqkVwxCvpSN/KTbBxH0Xv+Hw2t/lMpGsnb3UVGbrqqyi4GkOwS/GjUdoaYN29s7PHj9vd43jz7uamOHRqyvSs9nsRWef39dvnOVMbOnTu2smB4WDpxwr7/UV2dfuy8nTtUuf4WxWJSv1Otwb//O1WuvT4+9sQJezuVlWPpnbGYvQ0p8Z3IqYwdGLD/ljlz7HjJPi7Hj099bHW1/TdK9jEfHLSPwdy5Y7cx+v2cythsvveZxtb+o318nVhMEadGA5vvV8Wa6zN+P0/m5yTd9346Pyfpvp9TGTuV7/3J/JxU7Nyl39uwTh4Tk/F41Pc/v67+61bn5Odk/PczFz8nxfYcMdj+TVV89g7NM/3yeoyibVs08KmmaX/veY4YObeHdkqf+bwqzKDmegZtC6Kbmqb0vec5Iv3Yim07NGfdLeo382Qcjyra7tXwp5sSvp88R5z8c0TFNvs37USsUsNOhZyt90k3fyrt2FE8R9jrmZ4jTnlkh+Z9xr5eiDqV6tu8RebG60/6e89zxNhYbdulmg23aq4ZkPF4NPD1Ler9hH1eSPf9nMrPybxdOxWNtdqVxMs9uS2u9+6NF/OSLYUqdu5Szc5d8UlOJxaT1q6VGhtL4k0gx5hxqWlI0dvbK5/Pp3A4rPnz5xf6dLLnujKBQMKS+yFHOnODTXfMm03HpIHfk24JSr8/slf/ufXS7q9L535b+vjHx8b+nSu9WSetfaf0B/9hj/2iSfr/tkvB70nXXzU29n++KPUEpU+vlM54xh771TXSt78tBX4k3XT52Nhv/EL6zTul1R+Qzv53e+zFD0rf+p60eK/U8u6xsaGnpaMrpU98RFr+/9ljL18m7fiR9NZfSa3njY19+Enpvz6gBX98vX77b9+S10h7dYHerb0K6LCGPnfW2GP7j49Lhz4ifWiNdP5D9tgb50ptv5Kqfyt9YeHY7X7nm9Ivr5caN0gX/b09diwg/f1haU5E+vPasbH/0iH97zXSqj+XLr3HHoucKn31t/b63c7Y2O8/IP18g3TJV6T3/YU9Fq2W7hn5K/ilGqly5Nn2B38j/eTPpQs3S3/yubHbuHvk6eHzb5Vq/q+9/uMvST/8ivRHD0pXt4yN/UqfNFgjffZMacERe+xnn5X+bbP09l3S/7hhbOx9b0jH3yqtf5u08KA9tu9m6V8f1Lyz/1l9//VReUfu+ky9rCM6U2/95Ar9dtnz9uB/Xif9v7ukJU9Jn7pi7Ha/fkD67dukpgbprD322Asflv7pn6XTfyo1v3dsbMdz0qsrpOuulJbutsf+z/ulnU9Jp+2X1r1rbOy2TulIg3TttdLbHrPHXrlY+l8/ld7SJd06btnWru9KXVdKH75RetcOe+y1d0jt+6VTuqXbx/3hePRR6eC10gdbpXe32WP/XS9t6ZLm/k66a8HY2Me3Sf9xo/SBz0srv2aP9S6W7u+WPIPSxsqxsd/bKu1tlS67W7r8r+yxfp907+8kSVHN0RzZxq+36z7dr89LF39VuuILduxwhfT/jIRhfPH3pKqwvd75l9Keu6UVX5eu/MzY/f11VIrNkW6rk+a/ao/99A7pqa9K79guffSmsbEl+hxRF5bOeeBJ/UAf0Dd1va7XtzTkSIv/9AL99h/3Sr7D0ufOGrtdniPssSyfI+rC0pcfuFl/pgf1Yf2z/lkfHfub9r9elsJnSmtWSHU8R0z1OaLuj/5KRzZLbxqfFuh3kqTjmqPg54bs37Qn75Oe4TniZJ8j6m44Lz4r+AE9qX/XB7RD1+tLn/uWfXy7L5Ae5DlC0kk9R/yH3qY/lH0d8aBuVovs64gTqz86NvYBniMkTek5oubxrYr8R6v+UnfrbtnXEf9XPr115DlCX54jeUcayJ/Ec8Q6fV1tGvcc4fVKhw/npri+/37p9tuzG9vZKTU0TP8+8yTbOpRQvFKVJhSvwkj1PQU6nxKyKKJ4sTkej21u1ETTP77+3pk/l3LAH4HcCPZITtKxCsPPba4Ee1J/VvmblhvBntTn3Arx2OZKusfXKx7fXPGmOVZDt6Vp851IPZbLZd3Jfy81PJy70O5LLlHyy0gju1o5gdebl1yxQmCGPoNinqFXIJAQHWm8XvW/eFDGn9t9KuOV4lK5lNv9bbdOWb5cTiymYXl0QvMkj0dO1774Y8tSOXv9ZJbcV7z+qhacd078DanjqlLMUyHz6+flCdjHl6VyUx9rjNTf9aqq/vCPVGP64n9MBzzz1Psf/6mKMxeznHYazxGO2y3Vv0vGSHM1oAoNy3i96nvhoPpPrWM5rab3HOG43aqof7sGTYW8GtY8DcT/pkXeUsdyWp38c8TcN7pVFVwuxWI6LnvnVZ4BneiyrxdYcp/d2Im+9zU99vF1YjH1a55i8qjSM6TBrl/K+OtYcj+N5win+1W95Q+Xy2uG7VhVaMBTpeiBfZp79uL4WJbcW1N5joj+n1c1521/pEozoErZmfaYx6v//o8XZOoWT2vJ/dDhV3XKH/6h5plx7xrkcoZe0uCnblDFzl3xPfROU5MNx1u71j5gXq/U3j7r99BnXYcaTCocDhtJJhwOF/pUpu6hh4zxeo2R7P8feqjQZ1Q6eGzzi8c3f3hs84fHNr94fPOHxza/eHzzh8c2f/L42J74h6+bQUfGSCaWh+9b30CfueBmmc82yhx/es/YJ44eNaaz0/6/CGRbhzJDn0HRztCPcl27hKW+viRCH2YVHtv84vHNHx7b/OGxzS8e3/zhsc0vHt/84bHNnzw9tpFoRMvurFV9j7R74yFV57iFXCQaUe0mmx3Rd1efaiprMnzF7JRtHUpBn0HRF/QAAAAAMEvku+Aut4KePCQAAAAAAIoQBT0AAAAAAEUolx0IAAAAAAAoqLrwSMvTvfuk6LAUDJZsxgIFPQAAAACgJFRs26EjmyWvkcyOy+xBj0fq6Jj1repOBkvuAQAAAADFz3VVuf4WeUdi353R47GY7UPvuoU6s7yhoAcAAAAAFL+uLjmxWPrPDQ/bNnwlhoIeAAAAAFD8gkG7vD4dr1eqr5/Z85kBFPQAAAAAgOLn99u98l6vJGlk5b2M1yu1t5dkMB4FfTlwXamzM7d7RvJxmxjD45s/PLb5w2ObXzy++cNjmz88tvnF45s/PLZ5VReWGl6WHLc79zfe3CwdPqz+J3fr3TdLDU1S/4sHSzIQTyLlvvSFQjItLXJiMRmPR9G2LRq6qWlaN1mxbYcq19+S09vEGB7f/OGxzR8e2/zi8c0fHtv84bHNLx7f/OGxza/hhzrGUuh3Ls9P+rzfr9jCBXr+Gfuh8dfl9vZnEccYYzIPK1+9vb3y+XwKh8OaP39+oU9nalxXJhBICIYYcqQzN0jdvpO7ybqw4r+AubpNjOHxzR8e2/zhsc0vHt/84bHNHx7b/OLxzR8e2/xK9/jK65UOH875cvhINKLaTbWSpL67+lRTWZPT28+3bOtQltyXsjQpjxVGqu85+ZsM9iT9AubgNjGGxzd/eGzzh8c2v3h884fHNn94bPOLxzd/eGzzK93jW6rp8zOFGfoMSm2G3ni96n/x4EkvO3HcblUFl+f0NjGGxzd/eGzzh8c2v3h884fHNn94bPOLxzd/eGzzK93jywx9etnWoeyhL2V+v6JtW+Rd16oKY5+MnPZ2VS9ZevK3uWSp3eeydq19Ny0Xt4kxPL75w2ObPzy2+cXjmz88tvnDY5tfPL75w2ObX2ke33ymz9eF7aoAx+229+26UleXbW9XIon3zNBnUNQz9LLvTC27s1b1PdLujYdy92TkunZpTH19yfwyzCo8vvnDY5s/PLb5xeObPzy2+cNjm188vvnDY5tfM/D4DrS3qWJdqw3f83g0dP0nVbHrH+3qAI8nP2F8OZRtHUpBn0EpFPTFvNQEAAAAAKYk3dZjSc74MXla6p8rhOIBAAAAAMpPmnBwJ3lMiYTxUdADAAAAAEpHMGiX1Y+Tsizd67VL/oscBT0AAAAAoHT4/XaPvNdrP/Z6NbT6eg2NTNObPIfxzSRS7kvR+PTGhQtS0x0BAAAAoJQ1N0uNjfHwvejCBVp26q6RsPCDJdO5gIK+1IRCMi0tcmIxGY9Hnk9eoyPfkk133Ll81qc5AgAAAEBO+P1js/DRiLp9UrdPMv66wp5XDrHkvpS4bryYlyQnFtO8XY/KO7JhxInFbM9H1y3gSQIAAAAAcoGCvpSUUZojAAAAAJQ7CvpSEgzKlEmaIwAAAABMynWlzs74CuW6sNTw8ki2WImgoC8lfr+ibVsS0hudpqaEdMdSSXMEAAAAgAmFQjKBgLRqlUwgIM+nP60jm6XOHVJVcLkUChX6DHPCMcakTOJiTG9vr3w+n8LhsObPn1/o08koEo1o2Z21I+mNh2x6o+vG0x0p5gEAAACUNNeVCQQStiMbJW1H9nqlw4dnbX2UbR1Kyn0JSklvHJ/uCAAAAAClbCrZYkVeJ7HkHgAAAABQOsooW4yCHgAAAABQOsooW4yCvgRd4EobnpE8e/cV+lQAAAAAYMYN3dSkMzdIDU1S/4sHpe3b7Z75zk77/+bmwp5gjrCHvsRU3rxWz+20e0TMk5dJTU32hxcAAAAAykg5ZIsxQ19K9u5Vxc5d8cAHR5J27JD27i3gSQEAAAAA8oGCvpT85Cep6Y2S9NOfzvSZAAAAAADyjIK+lFxySWp6oyStXDnTZwIAAAAAyDMK+lKyYoWGVl8fL+qNZPfQr1hRwJMCAAAAgJnluN265oB07QF7vVRR0JeY6EPtevfN0oZG6cTTewjEAwAAAFBeQiFV1Z+jbz8mPfqYVFV/jhQKFfqs8oKCvgQ975f+/iIptuL8Qp8KAAAAAMwc15VZs0aOGduM7BgjrV0ruW4BTyw/KOgBAAAAAKWhqyuhmI8bHpZeemnmzyfPKOgBAAAAAKUhGJRx0vT+8nql+vqZP588o6AHAAAAAJQGv1/Rb2zV8PhjHo/U3i75/YU6q7ypKPQJILcct1vXHrAJ947bLS1ZWuhTAgAAAIAZM3RTk84+1KqLjko7P/qw5l16eUkW8xIz9KVlJM3x0cekb5d4miMAAAAATKTbJz12njR8zcdKtpiXKOhLh+vKtLSkpjm2tJRkmiMAAAAAlDsK+lLR1SUnFks9HouVZJojAAAAAJQ7CvpSEQzKeNJ8Oz2ekkxzBAAAAIA415U6O+Ork+vCUsPLI7liJYyCvlT4/Yq2bdHw+A4NjiN1dJT0nhEAAAAAZS4UkgkEpFWrZAIBeT79aR3ZLHXukKqCy0s6V8wxZtyma6To7e2Vz+dTOBzW/PnzC306k4pEI1p2Z60uOio9/NGHVVXCaY4AAAAAINeVCQQSth8bSQmd6L1e6fDhoqqNsq1DmaEvMaNpjrEST3MEAAAAgHRZYk7ymOHhks0Vo6AHAAAAABSnNFliKUvQvd6SzRWjoAcAAAAAFKeRLLGhkWl54/XKaWqyRbxk/9/eXrKrlysKfQLIrbqwFOwZSXOsrJa6uqRgsGR/gAEAAACUt6GbmnT2oVbV90i7Nx5U9ZKl0t/8jV1mX19f0rUQBX0Jqdi2Q0c2S14jmYfPsWEQxtjWdR0dUnNzoU8RAAAAAHKu22cvxl9nD/j9JV3Ij2LJfalwXVWuv0XekQ0jjjG2mJekWExauzbekxEAAAAAUPwo6EtFmnTHBCWc7AgAAAAA5Ygl96UiGLRL6ycq6ks42REAAABAeSvXLDFm6EuF32/3yY+kORrH0fC4pMdSTnYEAAAAUL5Gs8Q6d0hV9efInHGGtGqVFAhIoVChTy+vHGNMSps+jOnt7ZXP51M4HNb8+fMLfTqZua700ks6fsZiLd26bCTp8ZBNegQAAACAUuK6MoHAxNuPvV7p8OGim9zMtg5lyX2pGUlzNNFIatIjAAAAAJSSbLPEiqygzxZL7gEAAAAAxWk0S2wiJZ4lRkEPAAAAAChOyVliHo+GRz5VDlliLLkHAAAAABSv5mapsVF66SX1J2SJHSz5LDEK+hKW0LphyVIbmFcm7RsAAAAAlJEyzRJjyX2JSmjdEFyuwU/dIBMIlE37BgAAAAAodRT0pch1Vbn+FnlHGhI6sZgqdu4aS3+MxaS1a+2MPQAAAACgKFHQl6I0rRuc5DGj7RsAAAAAAEWJgr4UpWndYJLHlHj7BgAAAAAodRT0pSipdYO8Xg2tvl5DI9P05dC+AQAAAECZcF2pszO+pbguLDW8PBIOXuJIuS9V41o3qL5e0YULtOzUXWXTvgEAAABAGQiFZFpa5MRiMh6PPJ+8Rke+JXmNZHYutxOdzc2FPsu8cYwxKauxMaa3t1c+n0/hcFjz588v9OmctEg0otpNtZKkvrv6VFNZU+AzAgAAAIBpcF2ZQCAhP8woKT/M65UOHy661cnZ1qEsuQcAAAAAFB/CwCnoAQAAAABFKBiUKfMwcAr6MjIaDuHZuy8hNAIAAAAAio7fr2jbloTwb6epKSEcvNTDwNlDn0Gp7KEfaG9TxbpWGw6hkaUoHk/Jh0QAAAAAKF2RaETL7qwdCf8+ZMO/XTceDl6sxXy2dSgp9+XAdVW5/hY5I2/dxPeVxGLS2rU2Db9If9ABAAAAlLdun70Yf5094PeXTX3DkvtykCYsIq7EQyIAAAAAoFRR0JeDYNAur0+nxEMiAAAAAKBUUdCXA7/f7pUfCYcYDU0wZRASAQAAAKB0OW63rjkgXXvAXi83hOJlUCqheJIk11X/C7/UpY9+UDWD40IjAAAAAKDYhEIya9bIGSlpjePIefDBkgj9JhQPqfx+xRYu0PPP2A/joREAAAAAUExcN6GYl2Svl1noN0vuAQAAAADFpasroZiPK7PQ77wX9Js2bZLjONqwYUP8mDFGd999txYvXqyqqio1NDToV7/6VcLXDQwM6JZbbtGpp56qmpoaXX311XJdN2HMsWPHtHr1avl8Pvl8Pq1evVq/+93vEsa88sor+tCHPqSamhqdeuqpuvXWWxWNRvP1zwUAAAAA5FswKOM4qcfLLPQ7rwX93r171dHRoT/8wz9MOH7ffffp/vvv19atW7V3714tWrRIH/jAB/Tmm2/Gx2zYsEGPP/64HnnkET399NPq6+vTVVddpeHh4fiY6667Tvv379cTTzyhJ554Qvv379fq1avjnx8eHtaVV16pSCSip59+Wo888oi+853v6Pbbb8/nP3vWqwtLDS+PC41wXamz0/4fAAAAAGY7v1/Rb2zV8PhjHk/5hX6bPHnzzTdNMBg0Tz31lLnsssvMZz/7WWOMMbFYzCxatMj87d/+bXzsiRMnjM/nM//wD/9gjDHmd7/7nZkzZ4555JFH4mO6u7uNx+MxTzzxhDHGmIMHDxpJ5tlnn42P+dnPfmYkmV//+tfGGGN2795tPB6P6e7ujo/5x3/8RzN37lwTDoez+neEw2EjKevxs92Jf/i6GXJkjGRiHo+Jrr7exDweYyRjPB5jHnqo0KcIAAAAABn1DfSZus/JXHONTP+uh405erTQp5Qz2daheZuhb21t1ZVXXqn3v//9Ccdffvllvf7667riiivix+bOnavLLrtMzzxj09r27dunwcHBhDGLFy/WeeedFx/zs5/9TD6fTxdeeGF8zHve8x75fL6EMeedd54WL14cH9PY2KiBgQHt27cv7XkPDAyot7c34VIyXFeV62+Rd2SriROLqWLnLjmxmD0Qi9kQCWbqAQAAABSBbp/02HnS8DUfK6+Z+RF5KegfeeQR/e///b+1adOmlM+9/vrrkqTTTjst4fhpp50W/9zrr7+uyspKLViwYNIxCxcuTLn9hQsXJoxJvp8FCxaosrIyPibZpk2b4nvyfT6fTj/99Gz+ycWhq2useB+RsuukzEIkAAAAAKBY5bygP3r0qD772c/qm9/8pubNmzfhOCcpwMAYk3IsWfKYdONPZsx4d911l8LhcPxy9OjRSc+pqASDdl/JOCm5kGUWIgEAAAAAxSrnBf2+ffv0xhtv6Pzzz1dFRYUqKiq0Z88e/c//+T9VUVERnzFPniF/44034p9btGiRotGojh07NumY3/zmNyn3/9vf/jZhTPL9HDt2TIODgykz96Pmzp2r+fPnJ1xKht8vdXTYol2SvF4Nrb5eQyPvbRivt/xCJAAAAAAUJcft1jUHpGsPjAv8LjM5L+jf97736Ze//KX2798fv1xwwQW6/vrrtX//fi1ZskSLFi3SU089Ff+aaDSqPXv26OKLL5YknX/++ZozZ07CmNdee00HDhyIj7nooosUDof13HPPxcf8/Oc/VzgcThhz4MABvfbaa/ExTz75pObOnavzzz8/1//04tDcLB0+bFPtDx9W9KF2nblBamiS+l88aD8PAAAAALNZKKSq+nP07cekRx+TqurPkUKhQp/VjHOMMSmrrnOtoaFB73znO7V582ZJ0r333qtNmzZp27ZtCgaDuueee/SjH/1Ihw4d0imnnCJJWrdunb773e9q+/btestb3qI77rhD//3f/619+/bJOzLD/Cd/8id69dVX1d7eLklqaWlRIBDQv/7rv0qybeve+c536rTTTtNXv/pV9fT06MYbb9RHPvIRbdmyJatz7+3tlc/nUzgcLq3Z+hGRaES1m2olSX139ammsqbAZwQAAAAAk3BdmTPOkJNcynq9dvKyBFYcZ1uHVszgOcV94QtfUH9/v9avX69jx47pwgsv1JNPPhkv5iXpgQceUEVFhT7+8Y+rv79f73vf+7R9+/Z4MS9Ju3bt0q233hpPw7/66qu1devW+Oe9Xq++973vaf369Vq5cqWqqqp03XXX6Wtf+9rM/WMBAAAAALnT1ZVazEtjAd8lUNBna0Zm6IsZM/QAAAAAMIswQx+Xtz70KB51YanhZcmzd5/dW08fegAAAACzld+v6De2anj8MY+nLAO+C7LkHrNHxbYdOrJZ8hrJ7LjMHvR4bBo+AXkAAAAAZqGhm5p09qFWXXRU2vnRhzXv0svLrpiXmKEvb66ryvW3yDuyUsUZPR6LSWvXMlMPAAAAYNbq9kmPnScNX/OxsizmJQr68tbVJScWS/+50UAJAAAAAMCsREFfzoJBu7w+Ha9Xqq+f2fMBAAAAAGSNgr6c+f12r/xIK8DRjEjj9ZZloAQAAAAAFBNC8cpdc7PU2Kj+F36pSx/9oGoGpd0bD6p6ydJCnxkAAAAAJHJdu3U4UKe6sBTskRy3WyrT+oWCHpLfr9jCBXr+Gfuh8dcV9nwAAAAAIFkoJNPSIicWU5Xj6BVjl5ybncvLtksXS+4BAAAAALOb68aLeUlyjIkXs04Zd+mioAcAAAAAzG6TdeiSyrZLFwU94urCUsPLI3tQJPsOV2dnWb7TBQAAAGAWCQZlJurQJZVtly4KekiSKrbt0JHNUucOqSq4XIOfukEmEJBWrZICASkUKvQpAgAAAChXfr+ibVs05NgPjeOMteAu4y5djjHGZB5Wvnp7e+Xz+RQOhzV//vxCn05+uK5MIJCwhMVIcsaP8Xqlw4fL8pcEAAAAQOFFohEtu7NW9T3S7o2HVF1ZbZfZ19eXXJ2SbR1Kyj3S7kdxkseM7kkpsV8UAAAAAMWj22cvxl8nVdaUfX3CkntIweDYcpURKcs2ynRPCgAAAADMVhT0sO9qdXTYol2SvF4Nrb5+bH9KGe9JAQAAAIDZiiX3sJqbpcbG+B6U6MIFWnbqrpH9KQdVvWRpoc8QAAAAQLlwXamry64mHjexWBeWgj0jnbmoUZihxzh+v9TQEP+F6fZJe84a2Z8CAAAAADMhFIp33DKBgAba2xSJRjT8UEdCZy46cVHQAwAAAABmC9eVaWmJh3Y7sZi861rV0Fqrms/cJu9I2JcTi0lr19qZ/DJGQQ8AAAAAmB3SdOCqMNLKVxQv5uNGO3GVMQp6AAAAAMDsEAzKJHfg8nq1aeOelON04qKgBwAAAADMFn6/om1bEjpuOe3tqlp5qZykzlx04iLlHuONT5JcuIAESQAAAAAzbuimJp19qDW141ZSZ65yL+YlCnqMCoXi4RPG45Hnk9foyLfsPhWzc7ntU9/cXOizBAAAAFAGun32ktJxy++nkB+HJfdImyQ5b9ejJEgCAAAAwCxGQY+0SZJO8hgSJAEAAADMkAtcacMzkmfvvkKfyqxGQY/0SZLJY0iQBAAAADADKm9eq+cekh54Upr33sukG28s9CnNWhT0SJ8k2dREgiQAAACAmbV3ryp27oqvGHYkaccOae/eAp7U7EVBD0k2SfLMDVJDk9T/4kFp+3bp8GGps9P+n0A8AAAAAPn2k5+kbv+VpJ/+dKbPpCiQco+4lCRJEiQBAAAAzKRLLpFRmkyvlSsLcDKzHzP0AAAAAIDZYcUKDa2+Pp7pZSSpqUlasaKAJzV7UdAjri4sNbwsOW536idd1y6/p3UdAAAAgDyKPtSud98sbWiUTjy9x24HRloU9JAkVWzboSObpc4dUlVwuQba2xSJRhSJRjTQ3iYTCEirVkmBgBQKFfp0AQAAAJSw5/3S318kxVacX+hTmdXYQw/JdVW5/hY5I+tanFhM3nWtOvtQqyTpyGbFP6dYTFq7VmpsZH89AAAAABQQM/SQurrkxGIJhyqMVN8jBXskb3JT+uFh6aWXZu78AAAAAAApmKGHFAxKHo+dfR9hvF7t3njQXt+5PLHg93ql+vqZPksAAAAAwDjM0MMune/osIW6JHm9ctrbVb1kqaqXLFW0bYuGRvpGGK9Xam9nuT0AAAAAFBgz9LCam+2++JdesrPv4wr2oZuadPahVtX3SLs3HlT1kqUFPFEAAAAAJcV1pa4uu3J4pA6pC9vtv47bLVF/TIiCHmP8/gln3rt99mL8dTN8UgAAAABKVigk09IiJxaT8XgUbdui4eEBHdlss7zMzuV2NXFzc6HPdFaioAcAAAAAzDzXjRfz0ki3rT9rVY0zFszt0GVrUuyhBwAAAADMvHTdtkSXramgoAcAAAAAzLxgUMaTWJIajyflGF22JkZBj4wct1vXHpCuOTASSgEAAAAA0+X3p3TUcjo65CR14KLL1sQcY0zyggaM09vbK5/Pp3A4rPnz5xf6dGZeKCSzZo2ckR8T4zhyHnyQUAoAAAAA0xaJRrTsztqRjlqHxjpquW7aDlzlIts6lFA8TGw0pGLcez6OMVJLC6EUAAAAAHIibUetSTpwYQxL7jGxNCEVkqRYjFAKAAAAACgwCnpMLE1IhSTJ4yGUAgAAAMDUua7U2Wn/P6IuLDW8TF7XyaCgx8RGQiqGnXHHHEfq6GD5CwAAAICpCYVkAgFp1SqZQEAD7W0afqhDRzZLnTukquByKRQq9FkWFULxMij3ULzRkIqLjkoPf/RhVV16OcU8AAAAgKlxXZlAIGFL75DsfGFC33mvVzp8uOxrjmzrUGbokVG3T3rsPCl2zcfK/hcLAAAAwElIk89VoaRiXpKGh8nrmgIKemSU9Z6WNPthAAAAACBdPpfxeFIzu7xe8rqmgIIek6rYtiNhT8tAe5si0UjKZaC9Lb4fRoEAe18AAAAAjBnJ5xoayecyXq+cjg45HR22iJfs/9vbWRU8Beyhz6Cs99Cn2+fiSGdusMvwR9WFpSOb2fsCAAAAYGKj+Vz1PdLujYdUvWSp/YTr2mX29fXUDyOyrUMrZvCcUGzS7XMxUn1PYkEf7Jlk7wu/kAAAAABGdPvsxfjrxg76/dQNJ4mCHhMLBm3P+XFFvfF6tXvjwYRfQMftltm5PLH4Z+8LAAAAAOQVe+gxMb/f9pwft6fFaW9X9ZKlqqmsiV+qlyxN2Q/D3hcAAAAAca4rz4/26AI3y8BtZIU99BmU9R76UVnsaZlwPwwAAACA8hYKybS0yInFZCQ5sgn3TkeH1Nxc6LObldhDj9zJck9L2v0wAAAAAMqX68aLeckW85Lsx2vXSo2NrOydBpbcAwAAAADyI03QdtxokDZOGgU9AAAAACA/gkEZzwRl5//f3t1Hx1nX+f9/XTMhITftbLHb1mZgaMik1K3uailYC22oLnEX9Lge/cldDTW2taSFLq4LrLvV9atG93jc/laNm9A5JRQUFXAPu9/qjyrZCkIFCiytxRLP9u6KVNSWKR1L0mQ+vz+uznTub9IkM9fk+ThnTsjMJ8kVvZq53tf7836/aaR9zgjoAQAAAAATw+9PbqAde55G2uOCGnoAAAAAwIQZWdWuS/Z3qvmY9KPVO1V7Opqz4TYKR0CPc2fb8ux7SZfZUsPpMyMo6HIPAAAA4IxYA+3o4kVSdX2pD6diENDj3JwZQVEbjeoZnRlBsW2BM7+eERQAAAAAMGGoocfY5RtBYdulOzYAAAAAqHAE9Bg7RlAAAAAAQMkQ0GPsGEEBAAAAIJFtS/39abt1G8NS64Ez/bYwbgjoMXaMoAAAAAAQEwrJBALSihUygYCGeroVGY5odEuvDm2W+vuk2uACKRQq9ZFWDMsYY/Ivm7pOnDghn8+ncDis6dOnl/pwyk5kOKL5dzUwggIAAACYymxbJhBIKskdsaQlHdKukORNjDq9XungQWKGHAqNQ+lyj3PGCAoAAABgisvQX6vKSEsPpwTz0tl+WwT054wt9wAAAACAc5Ohv5bxetW1aWd63y36bY0bAnqcs5wNLrI0xQAAAABQQVL7a3m9snp6VLt0mazeXieIl+i3Nc6ooc+DGvrchnq6VbWuU14jGY/H+Ue8ql2SVLW1T9W3bnC23ng8Um+v1NFR4iMGAAAAMBES+2tt37RfdU0tZ1+0bWebPf22ClJoHEpAnwcBfQ5ZGl9cvNH570ObaX4BAAAATBWR4YgauhokSSfvPql6+muNWaFxKFvuMXZZGl80H5OCx3I0vwAAAAAAnDO63GPsgkFnK31CUG+8Xm3ftM/5720LkgN+ml8AAAAAlcO2pYEBJy44swu3Mewk9yx7UErcco8JQYYeY+f3O3XxCQ0urJ4e1TW1qK6pJa0pBs0vAAAAgAoRCskEAtKKFTKBgIZ6ujW6pVeHNkv9fVJtcIEUCpX6KCseNfR5UENfgCwNLnI2xQAAAADgTpl6aUmyLHpojZdC41C23OPc+f1Z/5EO+pyH8TdO8kEBAAAAmBCZemlJUrYeWgT0E4Yt95hQWWfUM58eAAAAcKdgUMaTHEoajyftOXpoTTwCekyYqq19STU0Qz3digxHNNTTHa+3USBAbQ0AAADgJn5/Wr8sq7dXVkp/LXpoTTxq6POghn6MssyoX9Ih7QpRWwMAAAC4WdZ+WVn6a6E41NCjtLLMqF96OMd8ev7BAwAAAK6RsV9Wjv5aGH9sucfEiM2oT2C8XnVt2kltDQAAAACMAwJ6TIwsM+prly5jPj0AAADgFjmaWWdtgI1JQw19HtTQn6MMNTTMpwcAAABcIBSSWbNGVjQq4/E4iblV7ZKk0S29ql9/h7zG6XBv9fZKHR0lPuDKUWgcSkCfBwH9+IsMR9TQ1SBJOnn3SdVX15f4iAAAAAAkydLk+uKNzn8f2kyj64lUaBzKlnsAAAAAQLIsTa6bj0nBYzkaXWNS0eUeJdEYdv4QWPaglLrl3ralgQGnsR53+AAAAIDJFww6W+kTgnrj9Wr7pn3Of29bkBzw0+i6JMjQY9JVbe3Toc1Sf59UG1ygoZ5uRYYjigxHNNTTLRMISCtWSIGAFAqV+nABAACAqcfvT2tmbfX0qK6pRXVNLU7NfEIDbBpdlwY19HlQQz/OqMUBAAAAXCFvM+sMDbAxPgqNQ9lyj8mVoxbHUo5aHP5AAAAAAJNu0Oc8jL8x/UW/n+v0EiOgx+QKBiWPR6IWBwAAAADOCTX0mFx+v5RSb5NYi5Nap0MtDgAAAFACti3Pf+/UZbbUeuBMM2uUHWro86CGfoJkqbfJW6cDAAAAYGKFQjJr1siKRmXklMYaj8dphNfRUeqjmxKooUd5y1Fvk7NOBwAAAMDEse14MC85wbwk5/O1a6W2NnbQlhG23AMAAAAAHBmaWMfFGlajbBDQAwAAAAAcwaCMJ0uYSMPqskNADwAAAABw+P3Jjapjz9OwuixRQ4+y0xiWlhyRvD94WFq+gj8aAAAAwCQaWdWuS/Z3qvmY9KPVO1V7OprWzBrlgYAeZaVqa58O/+uZrSMPtUuWJd1zD900AQAAgEkUa1QdXbxIqq4v9eEgC7bco3zYtqrXrU8+KY1xumnadqmOCgAAAADKEgE9ysfAgCxj0p+nmyYAAAAApCGgR/kIBp0t9qnopgkAAAAAaQjoUT78fumee2QSgnrj8dBNEwAAABgvti319+ctaW0MS60HJMsenKQDw1gQ0KO8dHTo1K9/pY9+RProR6RTAy/TEA8AAAAYD6GQTCAgrVghEwhoqKdbkeFI2mN0S68ObZb6+6Ta4AIpFCr1kSMLy5hMRcuIOXHihHw+n8LhsKZPn17qw5kSIsMRNXQ1SJJO3n1S9XTVBAAAAM6NbcsEArKi0fhTI5Z08Uanm31MY1g6tFnyJkaJXq908CC7ZidRoXEoGXoAAAAAqHQDA0nBvCRVGan5WPKy4LGUYF6iSXUZYw49ylJj2PljYtmDUlNL8ou2LQ0MOE30uEsIAAAA5BcMyng8SUG98Xq1fdM+GX9j/DnLHpTZtiA5+KdJddkiQ4+yU7W1L6lmJ7G2Z6inO173o0CAeh4AAACgEH6/hru/oZEz/aeN1yurp0d1TS2qr66PP+qaWmT19jpBvOR8pEl12aKGPg9q6CdZjtoeiXoeAAAAYKz++L+v6G83zNdbT0p3fnmnapcuy77Ytp1t9s3NXGuXQKFxKFvuUV5y1PZYylHPwx8ZAAAAILtQSLWrV6vnzPW0uapVuuee7BOl/H6usV2ADH0eZOgnmW07W+lTantOvbJPkrMFP62ehww9AAAAkJ1ty1x0kazU0I9r6bJFl3u4k98vpdTsxGp76ppa0up+qOcBAAAA8hgYSA/mJbrXVwAy9HmQoS+RLDU7keGI5t/VoOZj0vZN+1WX2gEfAAAAQDIy9K5Dhh7u5vdLra0Z/7gM+qSd85Q0XgMAAABAFn6/hr/9TY0mPufxsNu1AtAUDwAAAAAq3Miqdl2yv1NLjkjb/uY+nb/saoL5CkCGHq7TGJZaD0iWPeg8YdtSf7/zEQAAAEBGgz7poYXS6Ec+TDBfIQjo4SpVW/t0aLPU3+d0vD/98ZtlAgFpxQqnO34oVOpDBAAAAIBJQUAP97BtVd+6IT6L3opGVbXtgbNj7KJRae1aMvUAAAAApgQCerjHwEDyDHpJVuoaRm8AAAAAmCII6OEewaDTjTNB2sxFr9cZdQcAAAAAFY6AHu7h90u9vU7QLkler0ZW3qSRM2l64/UyegMAAABTUwGNotOaS8P1GFsHd+nokNranG31zc0anjVD82c+oOZj0vZN+1TX1FLqIwQAAAAmVygks2aNrGhUxuPRcPc3NLKqPWnJ6JZeHdoseY1kti1wEmUdHaU5XowbAnq4j99/Ngs/HJGUoZY+lW1LAwPOtn0y+AAAAKgUth0P5iWncbR3Xacu2d+pQZ+zpDGseDAfW6O1a51EGdfGrsaWe7ha6hi7oZ5uRYYjSY+hnm5G2wEAAKAyZWgcXWWk5mNnPw8eOxvMx9FMuiJYxpi0vmI468SJE/L5fAqHw5o+fXqpDweJbFsmEEj6AzZiSRdvVNa7kZKcGvyDB7kbCQAAAPfLcE1svF6demWfjL9RklMzXxtckBz4c01c1gqNQ8nQw724GwkAAICpzu93auYTGkVbPT2qa2pRfXW96qvrVdfUIiuluTTNpCsDGfo8yNCXMdt2ttBzNxIAAABTWGQ4ov/nlgb91YDU8Q8/UO3ffCTzQtuON5fmWri8kaFH5cswxi7T3cjUO5bcjQQAAEAlqf7kWv3Xd6X1z0nnf/ij0i23ZF7o90utrVwLVxAy9HmQoXeBPHcaI8MRzb+r4cxou/2MtgMAAEDlePZZmcsvT5/69Mwz0uLFpTgijINC41DG1sH9EsfYZTHocx6xrfgAAABARXjiicwjnH/+cwL6KYAt9wAAAADgVlddpYxbrpcunewjQQkQ0AMAAACAWy1erJGVN8WDeiNJ7e1k56cIAnoAAAAAcLHhLT26/JPSxjbpzSd3SvfeW+pDwiQhoAcAAAAAl3vOL/2/S6To4kWlPhRMIgJ6AAAAAABciIAeAAAAAAAXYmwdKp5lD+qje50GIZY9KDGHHgAAAEAFIEOPyhYKqbb5Un3/IekHD0m1zZdKoVCpjwoAAAAAzhkBPSqXbcusWSPLnJ3MaRkjrVkj2XYJDwwAAAAAzh0BPSrXwICsaDT9+WhU+vWvJ/94AAAAgGLYttTfX1AyqjEstR44U2KKKYOAHpUrGJTxZDjFPR6puXnyjwcAAAAoVCgkEwhIK1bIBAIa6ulWZDiS8TG6pVeHNkv9fVJtcAElplOIZUzCfmSkOXHihHw+n8LhsKZPn17qw0GRhnq6VfWpTnljT1iWdM89UkdH5i+wbWlgQAoGJb9/sg4TAAAAOMu2ZQKBpN2mI5Z08UZp0Je8tDEsHdoseROjOq9XOniQ61kXKzQOJUOPymc5H4xlaejL/0eRlddnvLM51NMdvwuqQIA7mwAAACiNDKWjVUZqPpa+NHgsJZiXpNFRSkynCDL0eZChdzHubAIAAMCNMlzHGq9Xp17ZJ+NvTFpq2YOqDS5IvgHAdazrkaEHuLMJAAAAt0hsgOf3a7j7GxqJ7TT1eGT19KiuqUX11fVJj7qmFlm9vU4QLzkfe3oI5qeIqlIfADBhgkGnAV7Knc3tmzLf2TTbMtzZpHkeAAAAJloo5IxbjkZlPB4Nd39DQ6NDqo8lnPJtqu7okNranGRUczPB/BTClvs82HLvcqGQtHatk22P3a3M0hBvqKdb3nWdqjJO4G/lWAsAAACMi0xlonJ6OVMOOnUVGoeSoUdlK+Ju5ciqdl2yv1PNx6Ttm/aprqllEg8UAAAAU1KmMlFJylYOSkCPBAT0qHx+f8F/+AZ9ziN1Sz4AAAAwIYJBp0Y+sUzU47Q6oxwU+dAUDwAAAABKJbUBntcrq7eXRncoCBl6AAAAACihrKWfNLpDHgT0AAAAAFBiGUs/iygdxdREQA8kaAw7M+k9z+6Whked0Xf8EQUAAABQhgjogTOqtvbp0GZnPIjpW+486fFIvb2MrwMAAABQdmiKB0iSbav61g3xWZ9W7Plo1Jljb9ulOjIAAABUItuW+vvj15mNYan1gGTZgyU+MLgJAT0gZZz/GReb+QkAAACMh1BIJhCQVqyQCQTk+cQndGiz1N8n1QYXSKFQqY8QLmEZY0ypD6KcnThxQj6fT+FwWNOnTy/14WCi2LYUCDgZ+VRer3TwILX0AAAAOHe2LRMIJM+dV8IOUYnrTxQch5KhByTnj2XCrM/YXS7DzE8AAACMpww7Q63UNewQRYFoigfEdHRIbW069fIeLfv+X6v+dMocUAAAAOBcBYMyHk/+DH1z82QfGVyIDD2QyO9XdPkyPeeXds5LmQMKAAAAnCu/X8Pd39DImQjeeL2y2tvjO0XFDlEUgYAeyCBvl9GUrqQAAABAoUZWtevijVJru3TqlX3Svfc6NfP9/c5HRiajQOMe0Hd1dWnx4sWaNm2aZs2apQ996EPav39/0hpjjD7/+c9r7ty5qq2tVWtrq375y18mrRkaGtKGDRs0c+ZM1dfX64Mf/KDslODp+PHjWrlypXw+n3w+n1auXKnXX389ac3hw4f1gQ98QPX19Zo5c6Zuu+02DQ8Pj/evjQoSm0cf6zI61NOtyHAk/hjq6Y53JVUgQBdSAAAAFG3Ql7Ij1O+XWlvJzKMo4x7Q79y5U52dndq1a5d27NihkZERXXPNNYpEIvE1//Iv/6Kvf/3r+uY3v6lnn31Wc+bM0V/+5V/qjTfeiK/ZuHGjfvjDH+rBBx/Uk08+qZMnT+q6667T6OhofM2NN96oF198UT/+8Y/14x//WC+++KJWrlwZf310dFTXXnutIpGInnzyST344IN6+OGH9elPf3q8f21UitR59NGovOs6Nf+uBjV0NWj+XQ2qWtd5tuaJOfUAAAAASmTCx9b97ne/06xZs7Rz504tW7ZMxhjNnTtXGzdu1J133inJycbPnj1bX/3qV7V27VqFw2H96Z/+qbZt26aPfexjkqTf/OY3uvDCC7V9+3a1tbXp5Zdf1tve9jbt2rVLV1xxhSRp165dWrJkiX71q19p/vz5+tGPfqTrrrtOR44c0dy5cyVJDz74oG655Ra99tprBY2hY2zdFNPf72TeU7S2O3dQWw84mfuMX9faOuGHBwAAAPeLDEfU0NUgSTp590nVV9eX+IhQbspmbF04HJYkXXDBBZKkAwcO6OjRo7rmmmvia2pqarR8+XI99dRTkqTdu3fr9OnTSWvmzp2rhQsXxtc8/fTT8vl88WBekt797nfL5/MlrVm4cGE8mJektrY2DQ0Naffu3RmPd2hoSCdOnEh6YAoJBiVP8j8L4/Vq+6b9Onn3Sf3fTftlUl6nCykAAACyytJ7KW/PJqAAExrQG2N0xx136Morr9TChQslSUePHpUkzZ49O2nt7Nmz468dPXpU1dXVmjFjRs41s2bNSvuZs2bNSlqT+nNmzJih6urq+JpUXV1d8Zp8n8+nCy+8sNhfG26WMo9eXq+snh7VNbWovrpedU0taV1J6UIKAACAjEKheO8lEwjEezONbulN6tlETyaM1YQG9OvXr9dLL72k7373u2mvWVbSpEUZY9KeS5W6JtP6saxJdPfddyscDscfR44cyXlMqEAdHTm7jKZ1JaULKQAAAFLZtsyaNfHeS7HeTK2dDapff0dSzyZ6MmGsJiyg37Bhgx599FH19/fLn5C9nDNnjiSlZchfe+21eDZ9zpw5Gh4e1vHjx3Ou+e1vf5v2c3/3u98lrUn9OcePH9fp06fTMvcxNTU1mj59etIDU1CeLqNpXUkBAACARAMDZxspn1FlpKWHFQ/m40ZHpV//evKODRVj3AN6Y4zWr1+vRx55RI8//rjmzZuX9Pq8efM0Z84c7dixI/7c8PCwdu7cqfe85z2SpEWLFum8885LWvPqq69q79698TVLlixROBzWM888E1/zi1/8QuFwOGnN3r179eqrr8bXPPbYY6qpqdGiRYvG+1cHAAAAAEcwmNZ7yXi96tq0k55MGDfjHtB3dnbq/vvv13e+8x1NmzZNR48e1dGjR3Xq1ClJzhb4jRs36stf/rJ++MMfau/evbrllltUV1enG2+8UZLk8/nU0dGhT3/60/rpT3+qF154QTfffLPe/va3633ve58kacGCBXr/+9+v1atXa9euXdq1a5dWr16t6667TvPnz5ckXXPNNXrb296mlStX6oUXXtBPf/pT/d3f/Z1Wr15N5h0AAADAxPH703ovWT09ql26TFZKzyZ6MmGsxn1sXbba9K1bt+qWW26R5GTx//mf/1k9PT06fvy4rrjiCn3rW9+KN86TpDfffFOf+cxn9J3vfEenTp3Se9/7XnV3dyc1qTt27Jhuu+02Pfroo5KkD37wg/rmN7+pP/mTP4mvOXz4sG699VY9/vjjqq2t1Y033qivfe1rqqmpKej3YWwdUkWGI5p/V4OCx6T/u2m/6ppanJqngQGnSz5/jAEAAKCz143Nx6TtsevGGNt2ttk3N3P9iDSFxqETPofe7QjokWqop1tV6zrlNZLxeDRy0w2qeuC7To2Ux+N0yadRHgAAwJTHvHmMVdnMoQcqim2r+tYNSV1Jq7Y9cLbhCV1KAQAAAEwSAnqgGBm6laYVmdClFAAAYGqxbWfkcYakTmNYaj0gWfZgCQ4MlY6AHihGMOhsq0+QVrNCl1IAAICpIxSSCQSkFStkAgEN9XQrMhxRZDii0S29OrRZ6u+TaoMLpFCo1EeLCkNADxTD73dq5BO6ko6svEkjZ142Hk/+LqU57uACAADARWxbZs2a+A5OKxqVd12n5t/VoPl3Nah+/R1JpZqUZmK8EdADxerokA4edILygwcVXfoeJQ53GBoZit+VTX0M9XTH7+AqEOAuLQAAgJtlKMesMlLzMSl4TPFgPo7STIwzutznQZd75GTbMoFA0h/yEUu6eKM06Ete2hiWDm1O+cPu9To3BxhVAgAA4D4ZrgWN16tTr+yT5GyzTwr4ufZDgehyD0yGHHdlU3GXFgAAoML4/Rru/oZGzuzWNF6vrJ4e1TW1qK6pRVZKqWbe0kygSGTo8yBDj5xs29k6n+GurPE3Ji217EHu0gIAAFSYyHBE8+9qUPMxafum/aprakleYNtOAqe5mWs+FIwMPTAZMjTJi92Vra+uT3rUNbWk3cHlLi0AAID7DfqknfOUltCR5FzrtbZyzYcJUVXqAwBcr6NDamsr6M7ryKp2XbK/88wd3H3pd3ABAABQXmxbGhhwxhdnuc5rDDvllZY9KHF9h0lEQA+MB7+/4Luugz7nkfEOLgAAAMpHKBQfS2c8Hme35ar2pCWxWfNeI5ltC5zdmx0dpTleTDkE9MAky3kHt4A7wAAAAJgEWWbMX7K/Mz7NKHWKUXzWfFsb13KYFNTQA5OoamufDm2W+vucMSZDPd3MqAcAAChHBUwzYooRSo0u93nQ5R7jJsfMeokZ9QAAAGUlx4z5WOkkU4wwUehyD5SbHHd5ubsLAABQZnLMmE+cYsSseZQSGfo8yNBj3OSYWS+Ju7sAAABlJu+M+RhmzWOckaEHyk2OmfXMqAcAACgh25b6+52PGVj5vp5Z8ygRMvR5kKHHuMtyB7fgO8AAAAAYPzlG041u6VX9+juckXQej7O9npF0mASFxqEE9HkQ0GOyRIYjauhqkCSdvPuk6qvrS3xEAAAAFY6mxShTbLkHAAAAgFxoWgyXqyr1AQA4qzHsvHlY9qAU23Jv29LAgBQMcjcYAABgPAWDzlb6lKbF2zc5TYvNtgxNi5ubJ/sogazI0ANlomprnw5tlvr7nI73Qz3dGurplgkEpBUrnA75oVCpDxMAAKBy5BhNx0g6uAE19HlQQ49Jkal+S5JlUbcFAAAwkfI2JmYkHUqg0DiULfdAOchUvyVJ2eq2eDMBAAAYN4M+52H8jekv+v1ce6FsseUeKAfBoORJ/udoPB6ZlOeo2wIAAChAnrnyqRrDUuuBM32MABchoAfKgd8vpdRoWb29aTVd1G0BAADkEQrFexCZQEBDPd2KDEeyPka39Cb1MaJnEdyEGvo8qKHHpEqp0cpb0wUAAICzU4EaGmTe/e6Mc+UHfelf1hhm1jzKEzX0gBtlqNHKWdMFAAAw1YVCMmvWyIpGZSxLVkq+MjZXPlNAn3PWPAE9XICAHihzGWfTJ2JOPQAAmKpsOx7MS5JljIwkK2GJkfSj1TsVXbwo7cste5BZ83A1auiBMpZpNn1izRdz6gEAwJSWYVKQlbLEklR7Oqr66vq0B7Pm4XbU0OdBDT1KJtNs+oQaMGq+AADAlJfheik1Q1/Q9RGz5lFmCo1DydAD5SrTbPozNWBSnpovAACAqcDvT5sKZLW3F59x9/ul1laCebgOGfo8yNCjZGzb2UafeMfZ69WpV/bJ+Btl2YOqDWao+cp2B5paewAAUIEyTgUi4w6XI0MPuF2m2fQ9PapraonXfI3cdINid+SMpNM3Xq/IrBlp81WptQcAAJVs0CftnJcwFYiMO6YIMvR5kKFHyWW7w5ynxj6GWnsAAFDJIsMRNXQ1SJJO3n1S9dX1JT4i4Nwxhx6oFBlm00vKWWOfGNAzXxUAAACoTAT0gFsFg5LHk1Zjv33TvrPbzcR8VQAAAKBSUUMPuFWeGvvE+aqp3V+ZrwoAAAC4Hxl6wM06OqS2trxdXEdWteuS/Z1nur/uc7q/AgAAlLMiJvQ0hp0yQ8selLjOwRRCQA+4XbYa+xSDPueRuB0fAACgLIVCMmvWyIpGZTweZ7fhqvaMS0e39MYbAJttC5wdjB0dk3u8QIkQ0ANTRM4718yoBwAA5cK248G8JFnRqLzrOnXJ/s6kxr9S+jQfKxqV1q51djByTYMpgBp6YAqo2tqnQ5ul/j6pNrhAQz3dzKgHAADlwbal/n7no5Rzkk+qnNN8gCmAOfR5MIcerpdjXr3EjHoAAFBCGbbWj/7l+1TbfKmshDDFeDw6NfByWumgZQ+qNphhmg/XMnC5QuNQMvRApctxl5u72gAAoGSybK1f3jVfqTlHyxjVVdclTfKJTfOxUqb+MM0HUwk19EClyzGvXlLxM+qptwcAAOMhS9Jh6eEMWUdjnIRDpmuPAqf+AJWIDD1Q6XLMq69ratHITTcodg/cSDp94/WKzJoRr7FPfFBvDwAAxk0wKONJDkeM16uuTTvTns+bcPD7pdZWgnlMOdTQ50ENPSqGbaffuc5RX5+vi6wkatQAAMA5Gerplnddp6qME8xbPT1Oxj0UcrrVj46e3UbPKDpMIYXGoWy5B6aKTPPqc9TXpwb0OevtCegBAMAYjKxq1yX7O9V8TNq+aZ/qYqN12UYPFISAHpjKctTXZ+oiW3S9PQAAQB6DPueReu2RMRkBIAk19MBUlqO+PlMX2eHub2jEcpYausgCAAAAJUWGHpjqitjSlnVbHAAAAIBJR0APoKgtbVm3xQEAAGSSZ+RtY9jp1WPZgxLJAqAobLkHAAAAMDFCofjIWxMIaKinO2kk7uiWXh3aLPX3SbXBBYzEBYpEhh4AAADA+LNtmTVr4g11rWhU3nWdumR/pwZ96SNxrWjUGVXX1kaPHqBAZOgBAAAAjL8c43GlPCNxARSEDD0AAACA8RcMyng8SUF94nhcRuIC544MPQAAAIDx5/enjbxNHI9b19QiK2V8LiNxgeKQoQdQlKROtNV1ObvWAgCACpeng/3IqnZd+Vynlh6Ruv7pcdUuXZa8oIjxuQDSEdADKFjV1r548xpz36UykixjJI9H6u113pQBAMDUEArFm94Zj8fJxq9qT1oyuqVXu0Jnrh12XJ35eqGI8bkAklnGmNRWFEhw4sQJ+Xw+hcNhTZ8+vdSHA5SObcsEAmnNbeK8XungQd6QAQCYCjJcF4xY0sUbpUGf83lqF3tJXC8ABSo0DqWGHkBhMnSqTZKvK61tS/39zkcAAOBueTrYS3SxByYDW+4BFCYYdLbWZwnqjWXp1EVzZYYjaa9Vbe1T9a0bnDd+tucDAOB+eTrYS6KLPTAJCOgBFMbvdwLxtWul0VGnfj7h5aiMWr45P77NLia23c6K3aGPRp3v0dbGdjsAANzqTAd777pOVZnkDvZxTS1J1w50sQfGH1vuARSuo8Ope/v615OCecnZUpe4zS6G7XYAALhclrK5kVXtWtIhbWyT3tz5eObdd7Frh/5+5yM79IBxRVO8PGiKB2Rg21IgkLT93ni9OvXK2W12MZY9qNpghu12NMQBAKD85ehkP7qlV/Xr73A62Hs8zkx5AnZgXBQahxLQ50FAD2QRCqVvocvyJj7U0522JY83fAAAylyOTvYSHeyBiVRoHEoNPYCx6ehw6uB//WunuU2ON++RVe26ZH+nmo9J2zftS66vAwAA5SlHJ3tLOUrqCOiBSUNAD2Ds/P6i3rRT6+6T2LY0MOB00+dCAACA0svRyV4SHeyBMkBTPAATrmprnw5tlvr7pNrgAg31dCsyHIk/hnq6ZQIBacUKpzY/FCr1IQMAgDOd7EfO3JFP7GRf19Ti1Mx7vc6LdLAHSoIa+jyooQfOUY76u0Hf2bF21OABAFB+IsMRzb+r4UzZ3P70sjnbLqj8DkBxqKEHUB5y1N8N+vKMtePCAACAkhv0OY/USTaSii6/AzC+COgBTKxgUPJ40kbcbd/kjLiz7EFq8AAAKIUC+9c0hp0b8JY9KNHYFigr1NADmFh+v5RSYxerv6uvrlddU0tafR41eAAATLBQKN6/xgQCaf1tYo/RLb1JfXDocwOUF2ro86CGHhgnOWrs8tbnAQCA8ZOnv00MfW6A0qGGHkB5KaDGjrF2AABMgjz9bWLocwOUPwJ6ACUXG2vnNc5M26Hub2hkVXvS69W3bnAuPjweZwt/R0fpDhgAADfLMV8+sfEdfW6A8seW+zzYcg9MsIkaa0dGHwAwFRX4/jfU0y3vuk5VGTnBfbab5aGQtHatk5mP9bnhpjow4dhyD8AdxjjW7tTLexSdNSPjtySjDwCYkkIhmTVrZEWjMh6P03Q2YcdbotHRIdXH3l9z5fc6OqS2NmbNA2WKDH0eZOiBCWbbUiCQNtbu1CvOtj/Ps7t1/pXLk+rrjaTLPyk9l+GaggY+AIApqcBGdxLvlYAbFBqHMrYOQGnlGWtXOzya1izPklR/OvO3y9nABwAAN7Ntqb/f+Zgqx463VLxXApWDDH0eZOiBSZJtrF2eDH4qyx5UbTBDAx+yDgAAN8uznd6yB1XbfKmshEt74/Ho1MDLae+XvFcC5Y8aegDukm2sXSyDn9CQJ5bBz6ipRUPd3zjb6OfMei5QAACuZdvxYF6SrGhU3nWdumR/Z3w7fWNYOmySR8Baxqiuuk6qrk/+fk0tae+t4r0ScCUCegDlr8iGPCOr2nXJ/k41H5O2b9qXPfgHAMANCpgbHzyWoZbWmOwz42l2B1QEAnoA7pAtg5/FoM95ZNqWDwCAqxQwN35MM+OLfG8FUH5oigcAAACUg2xN7/x+p2b+zH564/EkNZCtr65XXVOLM0s+ocks2+iBykdAD6AiNYal1gNOxiJJrg7BAACUSigkEwhIK1bIBAIa6ulWZDgSfwyNDsnKNze+o8NpbNff73zs6JikgwdQKnS5z4Mu94D7DPV0q2pdp7xGSZ2Aq7b2qfrWDc52RI/HaQjExQ4AoNTyzJBnbjww9TCHHsDUZNuqvnVD/KIn1gm4tbNBVes6z14sRaNOd18y9QCAUsszQ5658QCyoSkegMqS5aJo6eEcF0NkNwAApZSn6d2YGt4BmBLI0AOoLMGgs50+gfF61bVpp0zK81wMAQDKQmrTO683qekdDe8AZENAD6Cy+P1ObXzCRY/V06PapcvSLpa4GAIAlIuRVe26eKPU2i6demVfeo8XGt4ByIAt9wAqT0eH1NbmbKdvbo4H7SOr2nXlc51aeljq2vS4apcuy/z1ti0NDDjZfgJ+AMB4KeD9xcr19cyNB5CCDD2AyuT3S62tSRc+VVv7tCskbX5MOn/Z1WkjgSLDEQ31dMfHBikQkEKh0v0OAIDKkWcs3eiWXh3aLPX3SbXBBbz/ACgIY+vyYGwdUCHyjASSxjgWiGw+ACAfxtIBKBJj6wAgUZ6RQFL2sUCnXt6Tlsknmw8AKBhj6QBMEDL0eZChByqEbTtBd8pIoFOvOCOBJMnz7G6df+XypPpFI+nyT0rPpSRIyKYAAAqWIUOf+B5k2YOqDWYYS8d7CjBlkaEHgERZut/HRgLVV9erdng0rRmRJan+dPq3I5sCACgYY+kATBAy9HmQoQcqjG2ndb9Pei1PFj+m6GwKtfYAUJkK/PseGY6otbNBS49IXf+0M/OklVzvUQCmFDL0AJBJhu73Sa/lyeLHHnVNLRq56QbF7ogaSadvvF6RWTOotQeAqSJP5/rULva7QtLm/8+ZtJLxvSDXexQAZECGPg8y9MAUVEiGpICu+RK19gBQsQp8H5B4LwBQPDL0ADBWhWRICuiaL1FrDwCuZ9tSf7/zMVGB7wMS7wUAJk5VqQ8AAFwpGJQ8nrR6++2bkuvtLXtQZluGWvvm5sk8WgDAWIRCMmvWyIpGZTwep7HdqnZJkhVoVK1lyUrY7Go8Hm3f9HLGviu8FwCYCGToAWAsCqy3r2tqSetsTOdiAHAB244H85JkRaPyruvU/Lsa1NDVoJZvzldq5apljOqq6zL2XaGLPYCJQIYeAMaqo0Nqa8tbbz+yql2X7O9U8zFp+6Z9qmtqmeQDBQAULceW+kGfs40+LTNmjPOekOn9oMD3DAAoBgE9AJwLv7+gi7JBn/NI3YYJAChTwaCMx5MU1CeWVo1pG32B7xkAUCi23AMAAACp/P60kqnE0iq20QMoB2ToAaDUbFsaGHAa7RVyIVjsegDAmOQtmWIbPYASI6AHgEnQGHbqLS17UEq8IMzRQTmTqq19qr51g7PF0+NxGvN1dEzCbwAAU1Pekim20QMoIQJ6AJhgVVv7dGizM4PYbFugoTNBu2UPqnb16vjIIysaVdW6Tl2yv1ODvvTv0xiWDm2WrFhT5WhUWrvWyQ5xMQkAZ+XayfTss9ITT0hXXSUtXpz3W2W9IQsAZYAaegCYSLat6ls3yHsmCE8ce3TLnfOT5hdLTtC/5EjmbxU8pvj3iRsddbZ6AgAcoZBMICCtWCETCGiop1uR4YgiwxGd/vjNMpdfLn360zKXX67TH785/lqmx+iWXh3aLPX3SbXBBVIoVOrfDgCSWCZ1gCaSnDhxQj6fT+FwWNOnTy/14QBwm/5+acWKtKdb26U/jUg/eCj9S049cJ+iH/lw2vOWPajaYIaOygcPkqEHAMmZHR8IJP2dHLGkizdKb31DemaLZCUsN5Iu/6T0XIY/obFdUUk3UvmbC2CSFBqHkqEHgIkUDDq17gmcsUf71ffV/TKWlbzeslS77GrVV9enPeqaWtI6LtNRGQAS5Jgdf+Xh5GBecj5fyq4oAC5Ghj4PMvQAzlko5NS6j46eHWsUa2QXCklr1jj18AU0uYsMR9Ta2aClh6WuTTtVu3RZ5oV0wgcwFWXI0BuvV6de2Sfr1aM6/8rlaRn6N5/cqejiRWnfil1RAEqJDD0AlIuODucCsL/f+ZgYsHd0SIcOOa8dOpS3Y33V1j7tCkmbH5POX3Z1Um1o7DHU0x2vH1UgQM0ngKkjx+z42qXLZLUnTxGx2ttVu3RZ1l1RzJkHUO7I0OdBhh5A2chRGxrrik/NJ4CpLjIc0fy7Gs7Mjt+fPjv+2Weln/9cWrq0oC73sm3mzAOYdIXGoYytAwC3yFEbGgvoc9Z8ciEKYIrIOTt+8eLCAvkY5swDKGME9ADgFrEGeym1ods37YtftFr2oMy2DDWfzc3p3486ewAAAFejhh4A3MLvd5rmJdRzxmpDE2s+R266QbEkvZF0+sbrFZk1gzp7AO5m206/EdvOu7QxLLUecG5yAkAlo4Y+D2roAZSdXPWc1NkDcJNCdwqFQjJr1siKRmU8Hqfx3ar2jEtHt/Sqfv0d8hrJeDxOY7s8DUcBoNxQQw8AlSpXPSd19gDKQSGBeoFBumUPqnb1allnclBWNKqqdZ26ZH9n/O9aTOoNSysadcaGtrXx9w1ARSKgB4BKMt519hK19gCKU0CgXkyQ/tG90vdTbkJ6jbTkiPRQylpuWAKYagjoAaCSxOrs1651LmIT6uzjmlp0+qYbVLXtAVly6uxHbrxew7NmSMORpG9XtbVP1bducIJ/j8f53mxdBZCNbceDeckJ1L0ZAvVigvRstaH3/c19uvcjH056rugblgDgctTQ50ENPQBXOsc6e4laewAZ5Nux09/vNNtM0dou7Zx39vOP7JV+8FD6l5964D5FMwTptc2XxrP5zpOWdPhw5mMIhZJuaqqnhxuRAFyHGnoAmMrOsc5eYusqgBSFbKUPNKrWspKCb+PxaPuml5Nmwlv2oMzD6UF67bKrper65J/b1CLdc4+0Zo1TThTbLZTt71BHh1Mzn+2mJgBUEDL0eZChB1BxbNsZVZdSZ3/qlX1pF9y1wQxbV8nQA1NPETt7Dv9rylzkbNn0UCg9SM+VSc+18wgAKkyhcShz6AFgqilgnn1spv1w9zc0cubLjMfjbF3NdiFdxIxoAC6TY2dPouCxDBeXxjiBeKqODunQIefvxqFD+bfF+/1SayvBPAAkYMs9AExFRWxJtWKd8yQNjQxpJKVxnkTzPMD18tXGB4POTPccEzSkMTSly1UeBADIiy33ebDlHsCUNVHN8xiDB5SXAufBez7xCZ3/wPfj0zGs9nbp3nszfj+a0gHAuaEpHgDg3Jxj87xTL+9RdNaM5K8nkw+UlwLHzDWGpUPfkawzn1uSdP/90he/mH5jjqZ0ADBpCOgBAJkFg07QnWeLrefZ3TJ9y+MX+pKTvVv2/b/Wc0+dfS6WybdiwX806mTx2tq44AdKZaKmXrCVHgAmBQE9ACCzWPO8hK2zseZ5SYZH077UklR/Ovm5MY3Be/ZZ6YknpKuukhYvzn28bOUH0pWqNh4AMCkI6AEA2RWydbbATL5lD8rclzx32liWTl00VyZDo73qT65V1bYH4vW6Iytv0vCWnoyHyVZ+IINCauNnzZDnho8k18bffHP6jbumlrQbfDmnXgAAJgVN8fKgKR4AFKCQJli2LXPRRUkB/aglBTYmb+2VpMts6ZktStvGf/knpedS4oeim/IBU8FENrWkNh4AJhxz6AEAk6ejwwkA+vudj5my4wMDScG85AQRqXOsJenKw8nBvOR8vvRI+tqcW/mBqaqIufFF/fthFjwAlBUy9HmQoQeAcWLbUiCQtjX/1CvJW/Mlp9He+VemN9p788mdii5elLTWsgdVG8xQ20uGHlNZhgx9pn9v/PsBgPJEhh4AUF5iTfa8XufzhCZ79dX1SY/apcucGdcJrPZ21S5dlra2rqnFqQ0+E/0bansxFdi2syPGtjO/7vcn/7vweDL+e6trapGV8u+Sfz8A4B40xQMATJ5i5lPfe6/U2Sn9/OfS0qU5u9yPrGrXJfs71XxM2r5pX3pDL6CSFNLsTtLo6JDqY/swc23IZG48ALgWW+7zYMs9AJS/yHBEDV0NkqSTd59UfXV9iY8IGKN8Y+YmqtkdAKCssOUeADClNIal1gNOTXBG+bYoA8Uo5nwqdG0oJBMISCtWyAQCGurpVmQ4kvQ4te+liWl2BwBwJTL0eZChB4DyN9TTrap1nfIaZdyCzJx6jKsCt7xLRZx7BWbes410TG0YSbM7AHC3QuNQAvo8COgBoMzlCYTGtPU437ZnVK5x2vIuFXnu9fdLK1ak/bjWdmnnvITPD0j9fRmOu7/fGSeXKBSS1q51MvOxZnfcyAIAVyg0DqUpHgDA3XLM2x70Zd96fOrlPYrOmpH27cjmV6hCbtIUkHn37HtJtTnOt0TFnHtWoFG1liUrIc9iPB5t3/Ry2pg5sy1D5r25Of33odkdAFQ8MvR5kKEHgDKXZ759tpn2l39Sei4lvik6m08m3x0KCNQte1C1zZcmBdSjlhTYOLYt75KKPvcO/2tKcyPLkg4fTj+3yLwDQMUjQw8AmBpi8+0TApzYvG1J0vBo2pdYkupPp3+rYjKqZPJdwrbjwbwkWdGovOs6dcn+zqRA/aN7pe+n/H/vNdKSI9JDCesaTicH85Lzee3pqJQ6XaHIcy+tU7ExTnY9NaAn8w4AOIMMfR5k6AHAJWw7c4CTJ4OfqNCMKiPBXKTA2vSP7JV+8FD6l5964D5FP/Lh+OdFNZsr4tyjiR0AIBFj6wAAU4vf7zQFSw1+Yhl8r9f5PCGDX19dn/SoHR7NmH1NzaiOaSRYMWPOnn1W+vrXnY+5VOIovvEeBxcMyniSL3eM16vtm/br5N0n44++r+6XsVL+37cs1S67OukcqWtqkZVyPqmnJ3PQXcS5V9T3BQDgDDL0eZChB4AKkS2Dn7qmgIxq0dnUIsacVX9yraq2PSBLzu6AkZU3aXhLT9q6qq19ql633qn5tizpnntyb/mfiHr/Yr7nODWliymm5GGop1vedZ2qMs7/n1a2mvNQSFqzxvn/P18ZRSHn00SvBQBULMbWjRMCegCYYgpsOHb64zcXFHgX2mxNyt5wLdOW/9QGasaydOrXv0rbyi1NUL1/scF3vpsPEzUOTlJkOKL5dzWo+Zi0fdP+s/0VMiGgBgCUAZriAQAwFoU0HLNtVT3w3XjgbUmy7n9A82c+kBZ8FtpsTZKuPJy54drSI8kB/ZIj6TVzljFqv3O+HlqY/Hws+LVixxCNOjcs2trG3rm/wEZzsZ9/+F8Tfi9jZFav1qmrr0q6+TAe4+AyNpBLkPq/bUZ+P4E8AMA1COgBAEiVL6gbGEjebq/swWe2bXD3/c19ujeh2ZrkNOUzj6U35ev6p536UsJINO8PHpYeypwNT1VU8Ftg1r2Y4LvQmw+X2dIzSt+d8KPV6ePgLHtQ5r7kXQ/GsnTqorkyw5G04x3d0hvP6JttC5hIAACoGAT0AAAUKxh0tq6n1Npv35S5e7l5ODn4jDVbSxtztnSZ1N4u9fWdXdrertqly5LXLV/hbF1PDGg9HvV99WXdm+nnFxD8Wvagalevjq+zolFVZcm6FxN8F3rzoahxcNV1aTdKojJq+eb8vNvzrXw7FAAAcBECegAAihXrXp5Qax/rXp6mqcWpGU9ttpYtmLz3XqmzU/r5z6WlS6XFizP//HvuKeznFxj8FlMaUFTwXeDNB8selNmWodFgc3P67zQwkHyD5Myxjuf2fAAA3ICmeHnQFA8AkFWpu5cX8j3HeQ67NLYu/4U0Gix4HfPdAQAVji7344SAHgDgasWM4mtOLw3Q4cPnFqQnHkchNzQKXVfMzy/2WAEAKDEC+nFCQA8AcL1iMuSFzmGXSj/irdQ7JAAAmCAE9OOEgB4AUBHGO0MOAAAmDHPoAQDAWYXOV2cOOwAArpE6GhYAAAAAALgAAT0AAAAAAC5EQA8AAAAAgAsR0AMAAAAA4EIE9AAAAAAAuBABPQAAAAAALjQlAvru7m7NmzdP559/vhYtWqQnnnii1IcEAAAAAMA5qfiA/nvf+542btyoz372s3rhhRd01VVX6a/+6q90+PDhUh8aAAAAAABjZhljTKkPYiJdccUVete73qVvf/vb8ecWLFigD33oQ+rq6kpbPzQ0pKGhofjnJ06c0IUXXqhwOKzp06dPyjEDAAAAAKauEydOyOfz5Y1DKzpDPzw8rN27d+uaa65Jev6aa67RU089lfFrurq65PP54o8LL7xwMg4VAAAAAICiVHRA//vf/16jo6OaPXt20vOzZ8/W0aNHM37N3XffrXA4HH8cOXJkMg4VAAAAAICiVJX6ACaDZVlJnxtj0p6LqampUU1NzWQcFgAAAAAAY1bRGfqZM2fK6/WmZeNfe+21tKw9AAAAAABuUtEBfXV1tRYtWqQdO3YkPb9jxw695z3vKdFRAQAAAABw7ip+y/0dd9yhlStX6rLLLtOSJUvU29urw4cP61Of+lSpDw0AAAAAgDGr+ID+Yx/7mP7whz/oC1/4gl599VUtXLhQ27dvVyAQKPWhAQAAAAAwZhU/h/5cFTr/DwAAAACA8cAcegAAAAAAKhgBPQAAAAAALkRADwAAAACACxHQAwAAAADgQgT0AAAAAAC4EAE9AAAAAAAuREAPAAAAAIALEdADAAAAAOBCBPQAAAAAALgQAT0AAAAAAC5EQA8AAAAAgAsR0AMAAAAA4EIE9AAAAAAAuBABPQAAAAAALkRADwAAAACACxHQAwAAAADgQgT0AAAAAAC4EAE9AAAAAAAuREAPAAAAAIALVZX6AMqdMUaSdOLEiRIfCQAAAABgKojFn7F4NBsC+jzeeOMNSdKFF15Y4iMBAAAAAEwlb7zxhnw+X9bXLZMv5J/iotGofvOb32jatGmyLGvCf96JEyd04YUX6siRI5o+ffqE/zxgvHDuwo04b+FWnLtwK85duFEpzltjjN544w3NnTtXHk/2Snky9Hl4PB75/f5J/7nTp0/njxxciXMXbsR5C7fi3IVbce7CjSb7vM2VmY+hKR4AAAAAAC5EQA8AAAAAgAsR0JeZmpoafe5zn1NNTU2pDwUoCucu3IjzFm7FuQu34tyFG5XzeUtTPAAAAAAAXIgMPQAAAAAALkRADwAAAACACxHQAwAAAADgQgT0AAAAAAC4EAE9AAAAAAAuREBfRrq7uzVv3jydf/75WrRokZ544olSHxIqVFdXlxYvXqxp06Zp1qxZ+tCHPqT9+/cnrTHG6POf/7zmzp2r2tpatba26pe//GXSmqGhIW3YsEEzZ85UfX29PvjBD8q27aQ1x48f18qVK+Xz+eTz+bRy5Uq9/vrrSWsOHz6sD3zgA6qvr9fMmTN12223aXh4eEJ+d1SWrq4uWZaljRs3xp/j3EW5Ghwc1M0336y3vOUtqqur01/8xV9o9+7d8dc5d1GORkZG9I//+I+aN2+eamtr1dTUpC984QuKRqPxNZy7KLWf/exn+sAHPqC5c+fKsiz9x3/8R9Lr5XaO7tmzR8uXL1dtba0aGxv1hS98QWMePmdQFh588EFz3nnnmXvuucfs27fP3H777aa+vt4cOnSo1IeGCtTW1ma2bt1q9u7da1588UVz7bXXmosuusicPHkyvuYrX/mKmTZtmnn44YfNnj17zMc+9jHz1re+1Zw4cSK+5lOf+pRpbGw0O3bsMM8//7y5+uqrzZ//+Z+bkZGR+Jr3v//9ZuHCheapp54yTz31lFm4cKG57rrr4q+PjIyYhQsXmquvvto8//zzZseOHWbu3Llm/fr1k/M/BlzrmWeeMRdffLF5xzveYW6//fb485y7KEfHjh0zgUDA3HLLLeYXv/iFOXDggPnJT35ifv3rX8fXcO6iHH3xi180b3nLW8x//dd/mQMHDpgf/OAHpqGhwWzevDm+hnMXpbZ9+3bz2c9+1jz88MNGkvnhD3+Y9Ho5naPhcNjMnj3bXH/99WbPnj3m4YcfNtOmTTNf+9rXxvS7E9CXicsvv9x86lOfSnru0ksvNXfddVeJjghTyWuvvWYkmZ07dxpjjIlGo2bOnDnmK1/5SnzNm2++aXw+n/n3f/93Y4wxr7/+ujnvvPPMgw8+GF8zODhoPB6P+fGPf2yMMWbfvn1Gktm1a1d8zdNPP20kmV/96lfGGOcPsMfjMYODg/E13/3ud01NTY0Jh8MT90vD1d544w0TDAbNjh07zPLly+MBPecuytWdd95prrzyyqyvc+6iXF177bXmE5/4RNJzH/7wh83NN99sjOHcRflJDejL7Rzt7u42Pp/PvPnmm/E1XV1dZu7cuSYajRb9+7LlvgwMDw9r9+7duuaaa5Kev+aaa/TUU0+V6KgwlYTDYUnSBRdcIEk6cOCAjh49mnRO1tTUaPny5fFzcvfu3Tp9+nTSmrlz52rhwoXxNU8//bR8Pp+uuOKK+Jp3v/vd8vl8SWsWLlyouXPnxte0tbVpaGgoaSsqkKizs1PXXnut3ve+9yU9z7mLcvXoo4/qsssu00c/+lHNmjVL73znO3XPPffEX+fcRbm68sor9dOf/lSvvPKKJOl//ud/9OSTT+qv//qvJXHuovyV2zn69NNPa/ny5aqpqUla85vf/EYHDx4s+verKvorMO5+//vfa3R0VLNnz056fvbs2Tp69GiJjgpThTFGd9xxh6688kotXLhQkuLnXaZz8tChQ/E11dXVmjFjRtqa2NcfPXpUs2bNSvuZs2bNSlqT+nNmzJih6upqzn9k9OCDD+r555/Xs88+m/Ya5y7K1f/+7//q29/+tu644w79wz/8g5555hnddtttqqmp0cc//nHOXZStO++8U+FwWJdeeqm8Xq9GR0f1pS99STfccIMk/u6i/JXbOXr06FFdfPHFaT8n9tq8efOK+v0I6MuIZVlJnxtj0p4Dxtv69ev10ksv6cknn0x7bSznZOqaTOvHsgaQpCNHjuj222/XY489pvPPPz/rOs5dlJtoNKrLLrtMX/7ylyVJ73znO/XLX/5S3/72t/Xxj388vo5zF+Xme9/7nu6//3595zvf0Z/92Z/pxRdf1MaNGzV37ly1t7fH13HuotyV0zma6ViyfW0+bLkvAzNnzpTX6027s/jaa6+l3eEBxtOGDRv06KOPqr+/X36/P/78nDlzJCnnOTlnzhwNDw/r+PHjOdf89re/Tfu5v/vd75LWpP6c48eP6/Tp05z/SLN792699tprWrRokaqqqlRVVaWdO3fq3/7t31RVVZV0hzsR5y5K7a1vfave9ra3JT23YMECHT58WBJ/d1G+PvOZz+iuu+7S9ddfr7e//e1auXKl/vZv/1ZdXV2SOHdR/srtHM205rXXXpOUvougEAT0ZaC6ulqLFi3Sjh07kp7fsWOH3vOe95ToqFDJjDFav369HnnkET3++ONpW3vmzZunOXPmJJ2Tw8PD2rlzZ/ycXLRokc4777ykNa+++qr27t0bX7NkyRKFw2E988wz8TW/+MUvFA6Hk9bs3btXr776anzNY489ppqaGi1atGj8f3m42nvf+17t2bNHL774Yvxx2WWX6aabbtKLL76opqYmzl2UpaVLl6aNB33llVcUCAQk8XcX5euPf/yjPJ7kkMHr9cbH1nHuotyV2zm6ZMkS/exnP0saZffYY49p7ty5aVvxC1J0Gz1MiNjYulAoZPbt22c2btxo6uvrzcGDB0t9aKhA69atMz6fz/z3f/+3efXVV+OPP/7xj/E1X/nKV4zP5zOPPPKI2bNnj7nhhhsyjvfw+/3mJz/5iXn++efNihUrMo73eMc73mGefvpp8/TTT5u3v/3tGcd7vPe97zXPP/+8+clPfmL8fj8jaFCwxC73xnDuojw988wzpqqqynzpS18yAwMD5oEHHjB1dXXm/vvvj6/h3EU5am9vN42NjfGxdY888oiZOXOm+fu///v4Gs5dlNobb7xhXnjhBfPCCy8YSebrX/+6eeGFF+IjwMvpHH399dfN7NmzzQ033GD27NljHnnkETN9+nTG1lWCb33rWyYQCJjq6mrzrne9Kz5CDBhvkjI+tm7dGl8TjUbN5z73OTNnzhxTU1Njli1bZvbs2ZP0fU6dOmXWr19vLrjgAlNbW2uuu+46c/jw4aQ1f/jDH8xNN91kpk2bZqZNm2Zuuukmc/z48aQ1hw4dMtdee62pra01F1xwgVm/fn3SKA8gl9SAnnMX5eo///M/zcKFC01NTY259NJLTW9vb9LrnLsoRydOnDC33367ueiii8z5559vmpqazGc/+1kzNDQUX8O5i1Lr7+/PeG3b3t5ujCm/c/Sll14yV111lampqTFz5swxn//858c0ss4YYyxjzlTgAwAAAAAA16CGHgAAAAAAFyKgBwAAAADAhQjoAQAAAABwIQJ6AAAAAABciIAeAAAAAAAXIqAHAAAAAMCFCOgBAAAAAHAhAnoAAAAAAFyIgB4AAAAAABcioAcAAAAAwIUI6AEAAAAAcKH/H5XGBYYqX4b+AAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "((x1, y1), (x2, y2)) = biggest_rectangle(red_tiles)\n", "\n", "plot_tiles(breadcrumbs(red_tiles), figsize=(12, 12))\n", "plt.plot([x1, x1, x2, x2, x1], [y1, y2, y2, y1, y1], 'b:');" ] }, { "cell_type": "markdown", "id": "d7016370-a8b6-4d7a-9787-70a50b3207b9", "metadata": {}, "source": [ "We see that if the upper-left corner of the blue rectangle were any higher, then there would be red (and white) tiles in the upper-right corner of the rectangle. If the upper-left corner of the blue rectangle were any further west that would be ok, but would result in a slightly smaller area. You'll just have to take it for granted that all the possible rectangles formed below the equater lines are also a little bit smaller in area.\n", "\n", "Here's **one thing that bothers me**: suppose the two candidate corners on the east end of the equator were just one space apart from each other. Then there would be *no* white space between them, and a rectangle would be free to cross the equator. (If points were real-valued there would always be some space between them, but on a grid, it is possible to have no empty squares between two lines.) So if it is possible for two red tiles to be adjacent, then my `any_intrusions` algorithm could reject a valid rectangle. Now, it turns out there are no instances of adjacent red tiles:" ] }, { "cell_type": "code", "execution_count": 67, "id": "ff79f008-3ef4-43f0-a5fc-386fa5160d13", "metadata": {}, "outputs": [], "source": [ "assert not any(distance(p, q) == 1 for (p, q) in sliding_window(red_tiles, 2))" ] }, { "cell_type": "markdown", "id": "1ff570de-917a-488f-8b76-a814bfef4b20", "metadata": {}, "source": [ "But the instructions do not explicitly state that this is impossible, so my algorithm might fail on some inputs.\n", "\n", "Another thing that bothers me: if `find_possible_corners` doesn't find corners, will it still work? Let's check, by passing in all red tiles as the possible corners:" ] }, { "cell_type": "code", "execution_count": 68, "id": "d3b44691-da52-4794-ab77-bc4326aa6ca2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 3.69 s, sys: 83.8 ms, total: 3.77 s\n", "Wall time: 3.18 s\n" ] } ], "source": [ "%time assert biggest_rectangle(red_tiles, red_tiles) == biggest_rectangle(red_tiles)" ] }, { "cell_type": "markdown", "id": "b4e35203-687a-434e-88f5-0afea9f31c57", "metadata": {}, "source": [ "Yes, it finds the same maximal rectangle, but it takes a lot longer to find it.\n", "\n", "**Two final remarks**: One, this was the first puzzle of the year that was **difficult**. Two, my solution is **unsatisfying** in that it works for *my* input, and I strongly suspect that it would work for *your* input, because Eric Wastl probably created them all to be similar. But it may not work on every possible input allowed by the rules. " ] }, { "cell_type": "markdown", "id": "555e1ce1-9cf2-4f74-b5f4-9f94fb9ddaa0", "metadata": {}, "source": [ "# [Day 10](https://adventofcode.com/2025/day/10): Factory\n", "\n", "Today we find the machines in the factory are offline. Each machine has some lights, some buttons that can be pressed, and a joltage requirement for each light. For example, the machine described by:\n", "\n", " [.##.] (3) (1,3) (2) (2,3) (0,2) (0,1) {3,5,4,7}\n", "\n", "has four lights, and the goal configuration `.##.` means that the second and third light should be on and the others off. There are six buttons (each delimited by parentheses): the first button toggles light number 3, the second toggles lights 1 and 3, and so on. (The machine uses 0-based indexing.) Finally, the joltage requirements for the four lights are `3,5,4,7`. We can parse the input lines into machine descriptions like this:" ] }, { "cell_type": "code", "execution_count": 69, "id": "84cd63a7-4d50-4f14-9807-3cb439f80c88", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Puzzle input ➜ 165 strs of size 30 to 209:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "[.##....#..] (0,1,3,4,5,6,7,8,9) (0,1,2,4,5,6,7,8,9) (0,1,2,4,6,7,9) (1,2,3,5,7,8,9) (1,3,8) (7) ...\n", "[..#.....#] (0,2,4,6,7) (0,4,6,7) (0,1,2,5,7,8) (0,3,5,8) (0,1,2,3,4,7,8) (3,5,7) (3,6) (0,1,2,3 ...\n", "[.#....###] (4,7) (2,6,7,8) (0,1,2,4,6,7,8) (0,5) (5,8) (1,4,5) (0,2,3,5,6) (2,4,5,8) (2,3) (0,6 ...\n", "[.###.##.##] (1,3,4,6,7,8) (0,1,2,4,8) (1,2,5,6,8,9) (3) (0,2,4,8) (1,4,5,6) (2,4,6,8,9) (0,1,3, ...\n", "[#.##..###.] (2,3,5,7,8) (4,5) (0,1,2,4,5,7) (2,6,7) (2,3,4,5,6,7,8,9) (0,3,5,6,8,9) (0,1,2,3,5, ...\n", "[#....] (0,2,3) (0,2,3,4) (2,3) (0,1,2) (0,3,4) (3) (1,2) {75,18,60,71,39}\n", "[##.##..] (1,2,3,4,6) (2,4) (0,1,3,5) (0,2,3,5) (0,1,3,4) {14,25,30,34,25,10,20}\n", "[...#.#] (0) (1,4) (3,5) (2,4) (0,1,2,3) (1,2) (0,1,2,4) {50,56,62,34,48,17}\n", "...\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Parsed representation ➜ 165 tuples of size 3:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "('.##....#..', ((0, 1, 3, 4, 5, 6, 7, 8, 9), (0, 1, 2, 4, 5, 6, 7, 8, 9), (0, 1, 2, 4, 6, 7, 9), ...\n", "('..#.....#', ((0, 2, 4, 6, 7), (0, 4, 6, 7), (0, 1, 2, 5, 7, 8), (0, 3, 5, 8), (0, 1, 2, 3, 4, ...\n", "('.#....###', ((4, 7), (2, 6, 7, 8), (0, 1, 2, 4, 6, 7, 8), (0, 5), (5, 8), (1, 4, 5), (0, 2, 3, ...\n", "('.###.##.##', ((1, 3, 4, 6, 7, 8), (0, 1, 2, 4, 8), (1, 2, 5, 6, 8, 9), (3,), (0, 2, 4, 8), (1, ...\n", "('#.##..###.', ((2, 3, 5, 7, 8), (4, 5), (0, 1, 2, 4, 5, 7), (2, 6, 7), (2, 3, 4, 5, 6, 7, 8, 9) ...\n", "('#....', ((0, 2, 3), (0, 2, 3, 4), (2, 3), (0, 1, 2), (0, 3, 4), (3,), (1, 2)), (75, 18, 60, 71 ...\n", "('##.##..', ((1, 2, 3, 4, 6), (2, 4), (0, 1, 3, 5), (0, 2, 3, 5), (0, 1, 3, 4)), (14, 25, 30, 34 ...\n", "('...#.#', ((0,), (1, 4), (3, 5), (2, 4), (0, 1, 2, 3), (1, 2), (0, 1, 2, 4)), (50, 56, 62, 34, ...\n", "...\n" ] } ], "source": [ "def parse_machine(line: str) -> tuple:\n", " \"\"\"Parse a line into lights, buttons, joltage.\"\"\"\n", " lights, *buttons, joltage = line.split()\n", " return lights[1:-1], mapt(ints, buttons), ints(joltage) \n", " \n", "machines = parse(10, parse_machine)" ] }, { "cell_type": "markdown", "id": "d5d91403-5dc4-4fb5-be36-58a1e45e9eab", "metadata": {}, "source": [ "### Part 1: What is the fewest button presses to configure the lights on all the machines?\n", "\n", "The lights are initially all off, and we want to get them to the goal configuration with the minimum number of button presses. It makes no sense to press any button twice; that just toggles lights on and off and we end up where we started. So we want to find the smallest subset of buttons that when pressed gives the goal light configuration. The function `powerset` (from the [itertools recipes](https://docs.python.org/3/library/itertools.html#itertools-recipes)) yields subsets in smallest first order, so just look for the first subset of the buttons that toggles every light the proper odd/even number of times. " ] }, { "cell_type": "code", "execution_count": 70, "id": "179e62b1-e4cb-43e4-8dc7-b87a28d21e8d", "metadata": {}, "outputs": [], "source": [ "def minimal_button_presses(machine) -> int:\n", " \"\"\"How many button presses to configure lights on this machine?\n", " First try all ways of pressing 1 button, then all ways of pressing 2, ...\n", " Return as soon as one way matches the goal configuration of lights.\"\"\"\n", " lights, buttons, joltage = machine\n", " goal = [\".#\".index(ch) for ch in lights] # i.e., lights = \".##.\" ⇒ goal = (0, 1, 1, 0)\n", " for pressed in powerset(buttons):\n", " # Check that total presses for each light mod 2 is equal to goal for that light\n", " presses = Counter(flatten(pressed))\n", " if all(presses[light] % 2 == on_or_off for (light, on_or_off) in enumerate(goal)):\n", " return len(pressed)\n", " return inf # Couldn't solve; return infinity" ] }, { "cell_type": "code", "execution_count": 71, "id": "d1368c2f-d792-4353-82e7-b0161ece784f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 10.1: .0533 seconds, answer 441 correct" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(10.1, 441, lambda:\n", " sum(map(minimal_button_presses, machines)))" ] }, { "cell_type": "markdown", "id": "ecd76248-e224-44fb-91cf-e843a0f4f8f3", "metadata": {}, "source": [ "### Part 2: What is the fewest button presses to configure the joltage levels on all the machines?\n", "\n", "In Part 2 we move a lever, and now the function of the buttons changes: they control the joltage levels of the lights, not the lights themselves. The joltage levels all start at zero. Pressing the button `(2, 3)` increments the joltage level of lights numbered 2 and 3 by one unit each. Our task is to get the joltage levels all exactly to the target levels in the minimum number of presses.\n", "\n", "My first thought when reading the puzzle description was \"*This is an [integer linear programming](https://en.wikipedia.org/wiki/Integer_programming) problem.*\" My thought was confirmed by the instructions that said \"*You have to push each button an integer number of times; there's no such thing as 0.5 presses (nor can you push a button a negative number of times).*\" because having fractional or negative results is exactly what you might get from linear programming; you have to take extra steps to constrain the results to be non-negative and to be integers.\n", "\n", "Still, I was reluctant to use an integer linear programming package; that would mean that someone else is writing most of the code for the solution. This could also be seen as a search problem; I started programming an A* search solution, but it was way too slow. Why is it slow? Let's investigate. First, the number of buttons per machine is not too bad:" ] }, { "cell_type": "code", "execution_count": 72, "id": "1d2683fa-5126-4d2a-9dad-6a0e155f3449", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7.181818181818182" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean(len(buttons) for (_, buttons, _) in machines)" ] }, { "cell_type": "markdown", "id": "d7776686-d2a6-4645-b46b-86a7187ff6b5", "metadata": {}, "source": [ "The showstopper is the expected number of button presses per machine (total joltage requirements divided by average joltage added by each button press):" ] }, { "cell_type": "code", "execution_count": 73, "id": "a714c2c2-d433-41d0-8d1e-01832b35a1a9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "114.81498043610085" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mean(sum(joltage) / mean(map(len, buttons)) for (_, buttons, joltage) in machines)" ] }, { "cell_type": "markdown", "id": "fcbf4426-ce35-4270-aa51-7fcacdf86e24", "metadata": {}, "source": [ "That means a completely naive search would have to consider about 7115 possible button press sequences. Of course we can take advantage of the structure of the problem to make some optimizations to the search:\n", "1) Many joltage states will be repeated; we can cache them.\n", "2) Button presses are commutative; we can impose a canonical ordering.\n", "3) We can keep track of the best solution found so far and eliminate states that can't reach the goal in that number of presses.\n", "4) Some actions will be forced: if there is only one button that increments a given light, we *must* press it until the light hits its goal.\n", "5) If there are only two buttons that increment a given light, then the total presses of those two buttons must equal the joltage requirement for that light.\n", "6) And if there are three buttons that increment a given light, maybe we can somehow eliminate one button to get to two, and then to one.\n", "7) That process of button elimination is called [Gaussian elimination](https://en.wikipedia.org/wiki/Gaussian_elimination). Reluctantly, I will give in to the power of linear programming.\n", "\n", "A linear programming solver finds a solution **x** to the equation **A** **x** = **b** that minimizes **c** **x**, where **A** is a two-dimensional matrix and the other variables are one-dimensional vectors.\n", "\n", "For our problem we have:\n", "- **b** is the vector of joltage requirements for each light,\n", "- **c** says how much it costs to press each button, which is one press each so it is a vector of all ones,\n", "- **A** is a matrix where **A***i,j* says how much button *i* increments joltage *j* (each is either 0 or 1),\n", "- **x** will be the solution: a vector of number-of-pushes for each button.\n", "\n", "\n", "\n", "\n", "\n", "I started researching integer programming packages that run in Python. [Z3](https://github.com/Z3Prover/z3) seems to be the most popular, but it is a separate step to install it. I know that I (and many other people) already have **scipy** installed, and the [**scipy.optimize**](https://docs.scipy.org/doc/scipy/tutorial/optimize.html) package contains the function [**milp**](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.milp.html#scipy.optimize.milp), for \"mixed integer linear programming.\" The \"mixed\" part means that we can declare that some of the variables must be integers, while others can be continuous. (For our problem they will all be integers.)\n", "\n", "The arguments to **milp** are:\n", "- **c**: the cost vector (a 1 for every button in our problem).\n", "- **integrality**: indicates which variables must be integers; a 1 (True) for every button.\n", "- **constraints**: a linear constraint. I want to say **A** **x** = **b**, but in this package I have to say **lb** ≤ **A** **x** ≤ **ub**, where **lb** and **ub** are the lower and upper bounds on **b**. \n", "\n", "If we give it the right inputs, **milp** will magically return an optimal result for **x**. Here's how we get the data out of a `machine` and feed it to **milp**:" ] }, { "cell_type": "code", "execution_count": 74, "id": "713a1503-ae14-445f-91ea-714fcd618ad0", "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import milp, LinearConstraint, Bounds\n", "import numpy as np\n", "\n", "def minimal_joltage_presses(machine) -> int:\n", " \"\"\"The minimal number of button presses to set the joltage on this machine.\"\"\"\n", " lights, buttons, joltage = machine\n", " A = T([[int(i in button) for i in range(len(lights))]\n", " for button in buttons])\n", " ones = [1]*len(buttons)\n", " result = milp(c=ones, \n", " integrality=ones,\n", " constraints=LinearConstraint(A, lb=joltage, ub=joltage))\n", " return round(sum(result.x))" ] }, { "cell_type": "markdown", "id": "6ceb9e41-4e5e-442a-b162-db3384b07728", "metadata": {}, "source": [ "I made a few mistakes in not understanding the parameters of **milp**, but eventually I got it right and I was absolutely ***amazed*** at the speed:" ] }, { "cell_type": "code", "execution_count": 75, "id": "46d0d274-bd4c-44af-83e9-35c791a8e96b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 10.2: .1198 seconds, answer 18559 correct" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(10.2, 18559, lambda:\n", " sum(map(minimal_joltage_presses, machines)))" ] }, { "cell_type": "markdown", "id": "6be27520-1a83-42c9-841c-deb3f6422b4e", "metadata": {}, "source": [ "**This felt like cheating!** I only wrote a few lines of code, and **milp** did the rest. My main contribution was just recognizing that this was an integer programming problem.\n", "\n", "At least I can do a bit of analysis. One thing I was interested in: a system of linear equations can be determined, underdetermined, or overdetermined:\n", "- **Determined**: Same number of equations as variables (same number of buttons as lights); one unique solution.\n", "- **Underdetermined**: Fewer equations than variables (fewer buttons than lights); usually multiple solutions; we want the minimal one.\n", "- **Overdetermined**: More equations than variables (more buttons than lights); no exact solutions unless you are lucky (but for this puzzle Eric Wastl can make sure we are lucky every time).\n", "\n", "How under- or over-determined are the equations for our machines?" ] }, { "cell_type": "code", "execution_count": 76, "id": "b9f82fef-612b-48a5-9de1-6ff0b137f7fb", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Counter({-1: 68, 1: 65, 0: 32})" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Counter(sign(len(lights) - len(buttons)) for (lights, buttons, joltage) in machines)" ] }, { "cell_type": "markdown", "id": "a094063d-cd1d-446a-88c4-748d87506d92", "metadata": {}, "source": [ "This says that 32 machines are determined, 68 are underdetermined and 65 are overdetermined. By how much?" ] }, { "cell_type": "code", "execution_count": 77, "id": "e536441d-64d4-410d-bb40-2343f6e01d88", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Counter({-1: 32, -2: 31, 1: 34, 2: 31, 0: 32, -3: 5})" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Counter(len(lights) - len(buttons) for (lights, buttons, joltage) in machines)" ] }, { "cell_type": "markdown", "id": "541e9ab9-fdcd-4a06-be5a-3f6bac052652", "metadata": {}, "source": [ "Most by only 1 or two variables, but `(-3, 5)` means that 5 of the machines are underdetermined by 3 variables. Most of the time taken by **milp** must have been in searching for a minimal solution to these underdetermined cases." ] }, { "cell_type": "markdown", "id": "6ff8655e-d1cc-4524-b207-c1e425b2a408", "metadata": {}, "source": [ "Here are some tests on smaller machines that I used when I was unsure where my mistakes with **milp** were:" ] }, { "cell_type": "code", "execution_count": 78, "id": "b72544c8-6069-4310-a6dc-b4acd77981b4", "metadata": {}, "outputs": [], "source": [ "machine1 = parse_machine('[.##.] (3) (1,3) (2) (2,3) (0,2) (0,1) {3,5,4,7}')\n", "machine2 = parse_machine('[...#.] (0,2,3,4) (2,3) (0,4) (0,1,2) (1,2,3,4) {7,5,12,7,2}')\n", "\n", "assert 2 == minimal_button_presses(machine1)\n", "assert 3 == minimal_button_presses(machine2)\n", "\n", "assert 10 == minimal_joltage_presses(machine1)\n", "assert 12 == minimal_joltage_presses(machine2)" ] }, { "cell_type": "markdown", "id": "2e4af311-07cb-4777-ad81-7973ba5a3633", "metadata": {}, "source": [ "# [Day 11](https://adventofcode.com/2025/day/11): Reactor\n", "\n", "There are a bunch of servers here in the reactor room. Today's input consists of a list of device connectivity specifications; the line \"`wfc: ond mpw vsz`\" means that device `wfc` outputs to 3 devices, `ond`, `mpw`, and `vsz`. I'll capture the data like this:" ] }, { "cell_type": "code", "execution_count": 79, "id": "11e17f6a-acba-44c4-b704-7e4ff7471e7e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Puzzle input ➜ 643 strs of size 8 to 104:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "wfc: ond mpw vsz\n", "qxn: mow khk\n", "nzf: rti sqv\n", "ehm: von pgy fxk\n", "nlt: pdl hwf\n", "xqa: qvc cih\n", "ghq: ren\n", "jze: gbj\n", "...\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "Parsed representation ➜ 643 tuples of size 2 to 26:\n", "────────────────────────────────────────────────────────────────────────────────────────────────────\n", "('wfc', 'ond', 'mpw', 'vsz')\n", "('qxn', 'mow', 'khk')\n", "('nzf', 'rti', 'sqv')\n", "('ehm', 'von', 'pgy', 'fxk')\n", "('nlt', 'pdl', 'hwf')\n", "('xqa', 'qvc', 'cih')\n", "('ghq', 'ren')\n", "('jze', 'gbj')\n", "...\n" ] } ], "source": [ "devices = parse(11, atoms)" ] }, { "cell_type": "markdown", "id": "0ab28991-5875-4d2d-b6c5-eeef20ea8f81", "metadata": {}, "source": [ "### Part 1: How many different paths lead from you to out?\n", "\n", "We are asked how many distinct output paths there are from the device named `'you'` to the device named `'out'`. It is a simple recursive count, but I'll make two optimizations:\n", "- I'll convert the list of devices into a `dict`, for *O*(1) lookup instead of *O*(*n*).\n", "- It is likely that multiple paths will lead to the same intermediate devices, so I should memoize the counting function. (Note that a `dict` is not hashable and thus can't be in a `@cache`, so I make an inner function, `count`, and decorate that.)" ] }, { "cell_type": "code", "execution_count": 80, "id": "7540a982-988a-4822-af0d-6581f6f848c6", "metadata": {}, "outputs": [], "source": [ "def count_paths(devices, start='you', end='out'):\n", " \"\"\"How many distinct paths are there from start to end?\"\"\"\n", " lookup_table = {device: outputs for (device, *outputs) in devices}\n", " @cache\n", " def count(here, there) -> int:\n", " if here == there:\n", " return 1\n", " else:\n", " return sum(count(mid, there) for mid in lookup_table[here])\n", " return count(start, end)" ] }, { "cell_type": "markdown", "id": "95f75267-37e0-4ab4-949d-73956ea0450a", "metadata": {}, "source": [ "All very straightforward." ] }, { "cell_type": "code", "execution_count": 81, "id": "0c2d68a5-843b-49d6-aff6-23045968207f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 11.1: .0003 seconds, answer 574 correct" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(11.1, 574, lambda:\n", " count_paths(devices))" ] }, { "cell_type": "markdown", "id": "fdfb6e5a-99e5-4bcd-b31b-6dc051bca4c9", "metadata": {}, "source": [ "### Part 2: How many paths from svr to out visit both dac and fft?\n", "\n", "Now we are asked for a count of the paths from a different start device, `svr`, to the end device `out`, but the paths are constrained to visit some other devices along the way. That's easy; copy the structure from Part 1, but keep track of what other devices we still need to visit:" ] }, { "cell_type": "code", "execution_count": 82, "id": "0294e044-c7ef-418a-9c02-71615a453002", "metadata": {}, "outputs": [], "source": [ "def count_constrained_paths(devices, start='svr', end='out', others=frozenset({'dac', 'fft'})):\n", " \"\"\"How many distinct paths are there from start to end, visiting all the others?\"\"\"\n", " lookup_table = {device: outputs for (device, *outputs) in devices}\n", " @cache\n", " def count(here, there, others) -> int:\n", " others -= {here}\n", " if here == there:\n", " return (1 if not others else 0)\n", " else:\n", " return sum(count(mid, there, others) for mid in lookup_table[here])\n", " return count(start, end, others)" ] }, { "cell_type": "code", "execution_count": 83, "id": "677a97b3-183b-474e-87ba-7db0d6b763d8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Puzzle 11.2: .0031 seconds, answer 306594217920240 correct" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "answer(11.2, 306594217920240, lambda:\n", " count_constrained_paths(devices))" ] }, { "cell_type": "markdown", "id": "7f31ae9b-6606-40b0-9bb1-ed9b3fe3cbf0", "metadata": {}, "source": [ "# Summary\n", "\n", "Here are the run times and the correct answers for each of the puzzles:" ] }, { "cell_type": "code", "execution_count": 84, "id": "4d512a50-c6ae-4803-a787-b8f6e0103e31", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Puzzle 1.1: .0005 seconds, answer 1182 correct\n", "Puzzle 1.2: .0009 seconds, answer 6907 correct\n", "Puzzle 2.1: .0027 seconds, answer 23560874270 correct\n", "Puzzle 2.2: .0036 seconds, answer 44143124633 correct\n", "Puzzle 3.1: .0006 seconds, answer 17085 correct\n", "Puzzle 3.2: .0019 seconds, answer 169408143086082 correct\n", "Puzzle 4.1: .0538 seconds, answer 1569 correct\n", "Puzzle 4.2: .1409 seconds, answer 9280 correct\n", "Puzzle 5.1: .0073 seconds, answer 635 correct\n", "Puzzle 5.2: .0001 seconds, answer 369761800782619 correct\n", "Puzzle 6.1: .0015 seconds, answer 5877594983578 correct\n", "Puzzle 6.2: .0039 seconds, answer 11159825706149 correct\n", "Puzzle 7.1: .0007 seconds, answer 1681 correct\n", "Puzzle 7.2: .0014 seconds, answer 422102272495018 correct\n", "Puzzle 8.1: .6008 seconds, answer 24360 correct\n", "Puzzle 8.2: .6149 seconds, answer 2185817796 correct\n", "Puzzle 9.1: .0264 seconds, answer 4772103936 correct\n", "Puzzle 9.2: .0296 seconds, answer 1529675217 correct\n", "Puzzle 10.1: .0533 seconds, answer 441 correct\n", "Puzzle 10.2: .1198 seconds, answer 18559 correct\n", "Puzzle 11.1: .0003 seconds, answer 574 correct\n", "Puzzle 11.2: .0031 seconds, answer 306594217920240 correct\n", "\n", "Time in seconds: sum = 1.668, mean = .076, median = .003, max = .615\n" ] } ], "source": [ "summary(answers)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.15" } }, "nbformat": 4, "nbformat_minor": 5 }